Recent zbMATH articles in MSC 37https://zbmath.org/atom/cc/372024-11-01T15:51:55.949586ZUnknown authorWerkzeugOn the metric upper density of Birkhoff sums for irrational rotationshttps://zbmath.org/1544.110622024-11-01T15:51:55.949586Z"Frühwirth, Lorenz"https://zbmath.org/authors/?q=ai:fruhwirth.lorenz"Hauke, Manuel"https://zbmath.org/authors/?q=ai:hauke.manuelLet \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a \(1\)-periodic piecewise smooth function with rational discontinuities, i.e., there exist \(\nu\geq 1\) and \(0\leq x_1<\cdots < x_\nu<1\) with \(x_i\in \mathbb{Q}\) for all \(1\leq i \leq \nu\), such that \(f\) is differentiable on \([0,1)\setminus \{x_1,\dots, x_\nu\}\), \(f'\) extends to a function of bounded variation on \([0, 1)\), and there exists \(1\leq i \leq \nu\) such that \(f\) has a non-zero jump at \(x_i\). Let \(\alpha, q\in\mathbb{R}\). Set
\[
S_N(f, \alpha, q):=\sum_{n=1}^N f(n\alpha +q)- N\int_{[0,1)}f(x)dx.
\]
The present paper investigates the value distribution of \(\{S_N(f,\alpha, q): 1\leq N \leq M\}\) as \(M\to\infty\) for Lebesgue almost all \(\alpha\).
Let \(\psi: \mathbb{R}_+ \rightarrow \mathbb{R}_+\) be a monotone increasing function. Suppose \(q\in \mathbb{Q}\). The first main theorem of the paper proves that if \(\sum_{k=1}^\infty \frac{1}{\psi(k)}=\infty\), then for almost all \(\alpha\in [0,1)\), both sets
\[
\{N\in \mathbb{N}: S_N(f,\alpha, q)\geq \psi(\log N)\}, \quad \{N\in \mathbb{N}: S_N(f,\alpha, q)\leq -\psi(\log N)\}
\]
have positive upper density. If \(\sum_{k=1}^\infty \frac{1}{\psi(k)}<\infty\), then there exists a constant \(c>0\) such that for almost all \(\alpha\in [0,1)\), the set
\[
\{N\in \mathbb{N}: S_N(f,\alpha, q)\geq \psi(\log N)+c \log N \log\log N\}
\]
is finite. Further, for some special functions such as \(f(x)=\{x\}-1/2\), \(f(x)=\mathbf{1}_{[a,b]}-(b-a)\), and \(f(x)=\mathbf{1}_{[0,1/2)}-\mathbf{1}_{[1/2,1)}\), the above first two sets have upper density \(1\). This improves an old result of \textit{A. Khintchine} [Math. Z. 18, 289--306 (1923; JFM 49.0159.03)] on the discrepancy of the sequence \(\{n\alpha\}_{n\in \mathbb{N}}\).
The authors also prove some similar results for \(1\)-periodic functions with rational logarithmic singularities, that is, there exist constants \(c_1,c_2 \in \mathbb{R}\), a \(1\)-periodic function \(t : \mathbb{R} \rightarrow \mathbb{R}\) with bounded variation on \([0, 1)\) and \(x_1\in \mathbb{Q}\) such that \(f(x)=t(x)\) if \(x\equiv x_1 \mod 1\) and \(f(x)=t(x)+c_1\log(\|x-x_1\|)+c_2 \log(\{x-x_1\})\) if \(x\not\equiv x_1 \mod 1\).
On the other hand, let \(p_n/q_n\) denote the \(n\)-th convergent of the continued fraction of \(\alpha\). For \(N\in \mathbb{N}\), let \(K(N)\) be the integer \(K\) such that \(q_{K-1}\leq N< q_K\). Another main theorem of the paper shows that for almost all \(\alpha\in [0,1)\), the sets
\[
\Big\{N\in \mathbb{N}: S_N(f,\alpha, q)\gg \sum_{i=1}^{K(N)}a_i\Big\}, \quad \Big\{N\in \mathbb{N}: S_N(f,\alpha, q)\ll -\sum_{i=1}^{K(N)}a_i\Big\}
\]
have positive upper density, where the implied constants depend on \(\alpha, f\) and \(q\). This thus gives the sharpness of the classical Denjoy-Koksma inequality which asserts that
\[
|S_N(f,\alpha, q)| \leq \mathrm{Var}(f) \sum_{i=1}^{K(N)}a_i.
\]
Reviewer: Lingmin Liao (Wuhan)The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsionhttps://zbmath.org/1544.110772024-11-01T15:51:55.949586Z"Bénard, Léo"https://zbmath.org/authors/?q=ai:benard.leo"Frahm, Jan"https://zbmath.org/authors/?q=ai:frahm.jan"Spilioti, Polyxeni"https://zbmath.org/authors/?q=ai:spilioti.polyxeniLet \(X_1\) be the unit tangent bundle of a compact hyperbolic surface \(X\) with finitely many singular points \(x_1,\ldots , x_r\) of finite order. Let \(\rho:\pi_1(X_1)\to \mathrm{GL}(V_\rho)\) be a representation with \(\dim V_\rho = n \). The Ruelle zeta function \(R(s; \rho)\) is defined by \[R(s; \rho)=\prod_{\gamma\, \mathrm{prime}} \det \left (\mathrm{Id-\rho(\gamma)e^{s\ell(\gamma)}}\right),\] where \(\gamma\) runs through the prime periodic orbits and \(\ell(\gamma)\) denotes the length of the orbit \(\gamma\). For any \(j = 1,\ldots, r\), we denote by \(n_j = \dim \mathrm{Fix}\, \rho(c_j )\), so that \(\rho(c_j ) = I_{n_j} \oplus T_j\).
The main result of this paper under review is the computation of the behavior at zero of the Ruelle zeta function \(R(s; \rho)\). More precisely, the authors show that the Ruelle zeta function \(R(s; \rho)\) converges on some right half-plane in \(\mathbb{C}\) and extends meromorphically to the whole complex plane. Moreover
\begin{itemize}
\item If \(\rho(u) = \mathrm{Id}_{V_\rho}\) , then \(R(s; \rho)\) vanishes at \(s = 0\) with order and the leading coefficient is given as \(s\to 0\) by \[ R(\frac{s}{2\pi}; \rho) \sim \pm \frac{s^{n(2g-2+r)-\sum_{j=1}^r n_j}}{\prod_{j=1}^r |\det (I_{n-n_j}-T_j)|(-\nu_j)^{-n_j}}. \]
\item If \(\rho(u) \neq \mathrm{Id}_{V_\rho}\), then the representation \(\rho\) is acyclic. Let \(\mathfrak{e}_{\mathrm{geod}}\) be the Euler structure induced by the geodesic flow on \(X_1\). Then \[ R(0; \rho) = \pm \mathrm{tor}(X_1, \rho, \mathfrak{e}_{\mathrm{geod}}, \omega^1),\] where \(\mathrm{tor}(X_1, \rho, \mathfrak{e}_{\mathrm{geod}}, \omega^1) \in \mathbb{C}^\times\) denotes the Reidemeister-Turaev torsion of \(X_1\) in the representation \(V_\rho\), the Euler structure \(\mathfrak{e}_{\mathrm{geod}}\) and the natural homology orientation \(\omega^1\).
\end {itemize}
Reviewer: Sami Omar (Sukhair)Galois groups and prime divisors in random quadratic sequenceshttps://zbmath.org/1544.110952024-11-01T15:51:55.949586Z"Doyle, John R."https://zbmath.org/authors/?q=ai:doyle.john-r"Healey, Vivian Olsiewski"https://zbmath.org/authors/?q=ai:olsiewski-healey.vivian"Hindes, Wade"https://zbmath.org/authors/?q=ai:hindes.wade"Jones, Rafe"https://zbmath.org/authors/?q=ai:jones.rafeLet \(S\) be a fixed set of polynomials over the field \(K\), and let \(\gamma = (f_1, f_2, \ldots)\) be an infinite sequence of elements of \(S\). Let \(G_n\) be the Galois group of \(f^n :=f_1 \circ f_2 \circ \cdots \circ f_n\), assuming the latter is separable for all \(n\).
One can construct a rooted tree \(\mathcal{T}\) as follows: the root is \(0\in K\), the vertices of level \(n\) are the roots of \(f^n\) in \(\overline K\), and there is an edge between \(\alpha\) at level \(n\) and \(\beta\) at level \(n-1\) if and only if \(f_n(\alpha) = \beta\). Finally, let \(\mathcal{T}_n\) denote the tree truncated at level \(n\).
Then \(G_n\) acts on \(\mathcal{T}_n\), and \(G := \lim_n G_n\) acts on \(\mathcal{T}\). This is the *arboreal representation* defined by \textit{A. Ferraguti} [Proc. Am. Math. Soc. 146, No. 7, 2773--2784 (2018; Zbl 1442.11150)], which generalizes a classical construction in arithmetic dynamics (corresponding to the case when \(\gamma\) is constant and one iterates a single polynomial). Ferraguti has shown that, when the index of \(G\) in \(\mathrm{Aut}(\mathcal{T})\) is finite, one can deduce density results for the set of primes dividing all the \(f^n\) (in the case when \(K\) is a number field and the \(f_i\)'s have integer coefficients), among other applications.
In the present paper, the authors focus on the case when all polynomials in \(S\) are of the form \(x^2 + c\). First, they study a certain natural obstruction to the finiteness of the index of \(G\) in \(\mathrm{Aut}(\mathcal{T})\), and classify completely the occurrences of this obstruction (when \(K=\mathbb{Q}\)).
They further propose the definition of a *big arboreal representation*, a ``weaker and more approachable property than finite index''. They give probabilistic arguments showing in particular that this condition is satisfied with positive probability when \(K=\mathbb{Q}(t)\), and conjecture that the same holds over \(K=\mathbb{Q}\).
Reviewer: Pierre Guillot (Strasbourg)Differential equations. A dynamical systems approach to theory and practicehttps://zbmath.org/1544.340012024-11-01T15:51:55.949586Z"Viana, Marcelo"https://zbmath.org/authors/?q=ai:viana.marcelo"Espinar, José M."https://zbmath.org/authors/?q=ai:espinar.jose-mariaThe book is based on several graduate courses on ordinary differential equations, offered by the authors at Instituto de Mathemátika Pura e Aplicada in Rio de Janeiro. Its more elementary part includes formulations and proofs of standard facts of the ODE's theory: existence and uniqueness theorems, continuous and differentiable dependence on the initial conditions, continuations of the solutions, linear theory of ODE's, Lyapunov stability as well as methods for numerical integration.
The advanced part is devoted to the qualitative theory of ODE's, namelyé Poincaré maps, Poincaré recurrence theorem, topological classification of hyperbolic flows, Floquet's theorem, Lyapunov exponents, Grobman-Hartman and Poincaré-Bendixon theorems, stable manifolds, Poincaré-Hopf and Mayer's theorems.
Impressive historical remarks, specific references, huge Bibliography, a lots of exercises and an exemplary 48 hours graduate course of ODE's are applied.
Reviewer: Angel Zhirkov (Sofia)On periodic solutions for implicit nonlinear Caputo tempered fractional differential problemshttps://zbmath.org/1544.340092024-11-01T15:51:55.949586Z"Bouriah, Soufyane"https://zbmath.org/authors/?q=ai:bouriah.soufyane"Salim, Abdelkrim"https://zbmath.org/authors/?q=ai:salim.abdelkrim"Benchohra, Mouffak"https://zbmath.org/authors/?q=ai:benchohra.mouffak"Karapinar, Erdal"https://zbmath.org/authors/?q=ai:karapinar.erdalSummary: The main goal of this article is to study the existence and uniqueness of periodic solutions for the implicit problem with nonlinear fractional differential equation involving the Caputo tempered fractional derivative. The proofs are based upon the coincidence degree theory of Mawhin. To show the efficiency of the stated result, two illustrative examples will be demonstrated.On decaying and asymptotically constant solutions of nonlinear equations with the Weyl fractional derivative of an order in \((1, 2)\)https://zbmath.org/1544.340132024-11-01T15:51:55.949586Z"Řehák, Pavel"https://zbmath.org/authors/?q=ai:rehak.pavelSummary: We consider a sublinear fractional differential equation of an order in the interval \((1, 2)\) where the fractional derivative is of the Weyl type. Existence and asymptotic behavior of decaying and asymptotically constant positive solutions is studied. We mainly deal with regularly varying coefficients and/or solutions, but we also allow a more general setting. Our results are sharp and in the special case where the coefficient in the equation is asymptotically equivalent to a power function and the order of the equation is 2 we get back known results. An important role in the proofs is played by the fractional Karamata integration theorem and other properties of regularly varying functions, fixed point principle, and generalized fractional L'Hospital rule.Model reduction on manifolds: a differential geometric frameworkhttps://zbmath.org/1544.340192024-11-01T15:51:55.949586Z"Buchfink, Patrick"https://zbmath.org/authors/?q=ai:buchfink.patrick"Glas, Silke"https://zbmath.org/authors/?q=ai:glas.silke"Haasdonk, Bernard"https://zbmath.org/authors/?q=ai:haasdonk.bernard"Unger, Benjamin"https://zbmath.org/authors/?q=ai:unger.benjaminSummary: Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which emphasizes the geometric nature of the objects involved. The crucial ingredient is the construction of an embedding for the low-dimensional submanifold and a compatible reduction map, for which we discuss several options. Our general framework allows capturing and generalizing several existing MOR techniques, such as structure preservation for Lagrangian- or Hamiltonian dynamics, and using nonlinear projections that are, for instance, relevant in transport-dominated problems. The joint abstraction can be used to derive shared theoretical properties for different methods, such as an exact reproduction result. To connect our framework to existing work in the field, we demonstrate that various techniques for data-driven construction of nonlinear projections can be included in our framework.On the limit cycles of a class of discontinuous piecewise differential systems formed by two rigid centers governed by odd degree polynomialshttps://zbmath.org/1544.340212024-11-01T15:51:55.949586Z"Carvalho, Tiago"https://zbmath.org/authors/?q=ai:de-carvalho.tiago"Gonçalves, Luiz Fernando"https://zbmath.org/authors/?q=ai:goncalves.luiz-fernando"Llibre, Jaume"https://zbmath.org/authors/?q=ai:llibre.jaume(no abstract)Bifurcations analysis and monotonicity of the period function of the Lakshmanan-Porsezian-Daniel equation with Kerr law of nonlinearityhttps://zbmath.org/1544.340412024-11-01T15:51:55.949586Z"Lu, Lin"https://zbmath.org/authors/?q=ai:lu.lin"He, Xiaokai"https://zbmath.org/authors/?q=ai:he.xiaokai"Chen, Aiyong"https://zbmath.org/authors/?q=ai:chen.aiyongSummary: The bifurcations and monotonicity of the period function of the Lakshmanan-Porsezian-Daniel equation with Kerr law of nonlinearity are discussed. Firstly, by the traveling wave transformations, the Lakshmanan-Porsezian-Daniel equation is reduced to the planar Hamiltonian system whose Hamiltonian function includes a 6-\textit{th} degree polynomial. Then we give the phase portraits of the Hamiltonian system, and some traveling waves including dark wave solutions, kink and anti-kink solutions and periodic solutions are constructed by using the bifurcation method of dynamical systems. Furthermore, we discuss the monotonicity of the period function of periodic wave solutions by using some Lemmas proposed by \textit{L. Yang} and \textit{X. Zeng} [Bull. Sci. Math. 133, No. 6, 555--577 (2009; Zbl 1191.34055)]. Finally, some numerical simulations are presented.Global dynamics of a planar piecewise linear refracting system of node-node typeshttps://zbmath.org/1544.340442024-11-01T15:51:55.949586Z"Zhao, Hefei"https://zbmath.org/authors/?q=ai:zhao.hefei"Wu, Kuilin"https://zbmath.org/authors/?q=ai:wu.kuilin"Shao, Yi"https://zbmath.org/authors/?q=ai:shao.yi(no abstract)Nontrivial limit cycles in a kind of piecewise smooth generalized Abel equationhttps://zbmath.org/1544.340452024-11-01T15:51:55.949586Z"Zhao, Qianqian"https://zbmath.org/authors/?q=ai:zhao.qianqian"Yu, Jiang"https://zbmath.org/authors/?q=ai:yu.jiang"Wang, Cheng"https://zbmath.org/authors/?q=ai:wang.cheng.10(no abstract)On the 16th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systemshttps://zbmath.org/1544.340482024-11-01T15:51:55.949586Z"Li, Tao"https://zbmath.org/authors/?q=ai:li.tao.2"Llibre, Jaume"https://zbmath.org/authors/?q=ai:llibre.jaumeThe authors consider discontinuous piecewise polynomial Hamiltonian systems in two zones of the plane separated by the horizontal axis. An upper bound for the number of crossing limit cycles is provided by using the averaging method. Moreover, the upper bound is reached, as proven by the examples given.
Reviewer: Adriana Buică (Cluj-Napoca)Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic couplinghttps://zbmath.org/1544.340532024-11-01T15:51:55.949586Z"Arefev, Aleksei M."https://zbmath.org/authors/?q=ai:arefev.aleksei-m"Grines, Evgeny A."https://zbmath.org/authors/?q=ai:grines.evgeny-a"Osipov, Grigory V."https://zbmath.org/authors/?q=ai:osipov.grigory-v(no abstract)Influence of amplitude-modulated force and nonlinear dissipation on chaotic motions in a parametrically excited hybrid Rayleigh-van der Pol-Duffing oscillatorhttps://zbmath.org/1544.340642024-11-01T15:51:55.949586Z"Kpomahou, Y. J. F."https://zbmath.org/authors/?q=ai:kpomahou.yelome-judicael-fernando"Agbélélé, K. J."https://zbmath.org/authors/?q=ai:agbelele.k-j"Tokpohozin, N. B."https://zbmath.org/authors/?q=ai:tokpohozin.n-b"Yamadjako, A. E."https://zbmath.org/authors/?q=ai:yamadjako.a-e(no abstract)A conservative chaotic oscillator: dynamical analysis and circuit implementationhttps://zbmath.org/1544.340752024-11-01T15:51:55.949586Z"Parthasarathy, Sriram"https://zbmath.org/authors/?q=ai:parthasarathy.sriram"Natiq, Hayder"https://zbmath.org/authors/?q=ai:natiq.hayder"Rajagopal, Karthikeyan"https://zbmath.org/authors/?q=ai:rajagopal.karthikeyan"Zavareh, Mahdi Nourian"https://zbmath.org/authors/?q=ai:nourian-zavareh.mahdi"Nazarimehr, Fahimeh"https://zbmath.org/authors/?q=ai:nazarimehr.fahimeh(no abstract)Chaotic dynamics of a periodically forced Duffing oscillator with cubic quintic septic power nonlinearitieshttps://zbmath.org/1544.340782024-11-01T15:51:55.949586Z"Remmi, S. K."https://zbmath.org/authors/?q=ai:remmi.s-k"Latha, M. M."https://zbmath.org/authors/?q=ai:latha.m-m(no abstract)Existence of a cylinder foliated by periodic orbits in the generalized Chazy differential equationhttps://zbmath.org/1544.340882024-11-01T15:51:55.949586Z"Llibre, Jaume"https://zbmath.org/authors/?q=ai:llibre.jaume"Novaes, Douglas D."https://zbmath.org/authors/?q=ai:novaes.douglas-duarte"Valls, Claudia"https://zbmath.org/authors/?q=ai:valls.claudia(no abstract)Invariant tori via higher order averaging method: existence, regularity, convergence, stability, and dynamicshttps://zbmath.org/1544.340902024-11-01T15:51:55.949586Z"Novaes, Douglas D."https://zbmath.org/authors/?q=ai:novaes.douglas-duarte"Pereira, Pedro C. C. R."https://zbmath.org/authors/?q=ai:pereira.pedro-c-c-rFundamental research carried out by Krylov and Bogolyubov at the Institute of Structural Mechanics of the Academy of Sciences of the Ukrainian SSR (now S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine) laid the foundation for nonlinear mechanics as a new direction in mathematical physics. The averaging method in nonlinear mechanics is one of the main tools for the dynamic analysis of differential equations containing a small parameter. Important results in the development of the averaging method belong to Yu. A. Mitropolsky, J. Hale, Yu. A. Ryabov and others. In this article, the authors present results containing sufficient conditions for the existence of invariant tori in weakly perturbed systems of differential equations. In this case, the regularity, convergence and stability of such tori are investigated.
Reviewer: Anatoly Martynyuk (Kyïv)Existence and uniqueness of periodic solutions of a bioeconomic model of Fishery dynamicshttps://zbmath.org/1544.340922024-11-01T15:51:55.949586Z"Anjali, L. Dathan"https://zbmath.org/authors/?q=ai:anjali.l-dathan"Padhi, S."https://zbmath.org/authors/?q=ai:padhi.sidhartha-s|padhi.seshadev|padhi.saswat|padhi.sukanyaSummary: In this article we study the existence and uniqueness of positive periodic solutions of the following bioeconomic model in fishery dynamics \[\begin{cases}\frac{dn}{dt}=n\left(r(t)\left(1-\frac{n}{k}\right)-\frac{q(t)E}{n+D}\right),\\ \frac{dE}{dt}+E\left(\frac{A(t)q(t)}{\alpha(t)}\frac{n}{n+D}-\frac{q^2(t)}{\alpha(t)}\frac{n^2E}{(n+D)^2}-c(t)\right),\end{cases}\] where the functions \(r,q,A,c\) and \(\alpha\) are continuous positive \(T\)-periodic functions. The considered system of equations is a model of a coastal fishery represented as a single site with \(n(t)\) is the fish stock biomass, and \(E(t)\) is the fishing effort. We have used Schauders fixed point theorem and Banach contraction principle to show the existence of a unique nonegative \(T\)-periodic solutions of the above model. On the other hand, an application of Krasnosel'skii's fixed point theorem yields a sufficent condition for the existence of a positive \(T\)-periodic solution of the model. An example is given to strengthen our result.Interpolating asymptotic integration methods for second-order differential equationshttps://zbmath.org/1544.340992024-11-01T15:51:55.949586Z"Stepin, Stanislav A."https://zbmath.org/authors/?q=ai:stepin.stanislav-aThis paper is devoted to the problem of asymptotic behaviour at infinity of the solution of a second-order differential equation which can be reduced via the Liouville transform to an equation with almost constant coefficients. The authors compare various methods of asymptotic integration in application to the reduced equation
\[
u''-(\lambda^2 + \phi(t))u = 0\tag{1}
\]
and interpolate the corresponding results in the case \(Re \lambda > 0\), provided that a complex-valued function \(\phi(t)\) is in a certain sense small for large values of the argument.
The work consists of 6 paragraphs and a list of references. The first paragraph presents the formulation of the problem and its historical aspect, giving the main results -- Theorems 1 and 2. In paragraph 2, Lyapunov type functions are defined, as well as a suitable version of the retraction principle. In Section 3 some auxiliary integral estimates are given that will be used to prove the main results. Further, in paragraphs 4 and 5, the authors obtain a priori estimates for solving equation (1). These estimates are then used to asymptotically integrate equation (1).
A scheme of the transformation-based reduction method the first-order system to L-diagonal form is presented in Section 6. Section 7 applies the reduction method to the asymptotic integration problem under consideration. As a result, new conditions for the asymptotic equivalence of solutions to equation (1) and the corresponding comparison equation are obtained.
The work also provides examples of classes of functions \(\phi(t)\) that satisfy the conditions of Theorems 1 and 2.
The application of the results of Theorems 1 and 2 to obtain effective estimates is also indicated for the accuracy of the Liouville-Green approximation for the corresponding solutions of the equations of the type (1).
In my opinion, the results presented in the article are very important for the further study of asymptotic representations of solutions of second-order differential equation.
Reviewer: Olga Chepok (Odessa)Piecewise smooth perturbations to a class of planar cubic centershttps://zbmath.org/1544.341032024-11-01T15:51:55.949586Z"Peng, Linping"https://zbmath.org/authors/?q=ai:peng.linping"Li, Yue"https://zbmath.org/authors/?q=ai:li.yue"Sun, Dan"https://zbmath.org/authors/?q=ai:sun.dan.1(no abstract)Odd and even functions in the design problem of new chaotic attractorshttps://zbmath.org/1544.341152024-11-01T15:51:55.949586Z"Belozyorov, Vasiliy Ye."https://zbmath.org/authors/?q=ai:belozyorov.vasiliy-ye"Volkova, Svetlana A."https://zbmath.org/authors/?q=ai:volkova.svetlana-a(no abstract)A new four-dimensional chaotic system with multistability and its predefined-time synchronizationhttps://zbmath.org/1544.341192024-11-01T15:51:55.949586Z"Wang, Ertong"https://zbmath.org/authors/?q=ai:wang.ertong"Yan, Shaohui"https://zbmath.org/authors/?q=ai:yan.shaohui"Wang, Qiyu"https://zbmath.org/authors/?q=ai:wang.qiyu(no abstract)Bohr-Levitan almost periodic and almost automorphic solutions of equation \({x'(t)= f(t- 1, x (t - 1)) - f(t,x(t))}\)https://zbmath.org/1544.341302024-11-01T15:51:55.949586Z"Cheban, David"https://zbmath.org/authors/?q=ai:cheban.david-nikolaiSummary: This paper is dedicated to the problem of almost periodicity of solutions for functional differential equations \(x'=h(t,x_t) (*)\) when the right hand side is monotone with respect to spacial variable. The main results are established in the framework of general non-autonomous (cocycle) dynamical systems. We apply our general results to a class of delay differential equations \(x'(t)= f(t-1, x(t-1)) - f(t,x(t)) (**)\). In particular, we prove that every solution of equation (**) with Bohr-Levitan right hand side is asymptotically Bohr-Levitan almost periodic.
For the entire collection see [Zbl 1531.35008].Global Hopf bifurcation of state-dependent delay differential equationshttps://zbmath.org/1544.341322024-11-01T15:51:55.949586Z"Guo, Shangjiang"https://zbmath.org/authors/?q=ai:guo.shangjiang(no abstract)Existence and regularity of solutions for non-autonomous integrodifferential evolution equations involving nonlocal conditionshttps://zbmath.org/1544.341422024-11-01T15:51:55.949586Z"Zhu, Jianbo"https://zbmath.org/authors/?q=ai:zhu.jianbo"Yan, Dongxue"https://zbmath.org/authors/?q=ai:yan.dongxueSummary: In this article, we investigate the existence and regularity of solutions for non-autonomous integrodifferential evolution equations involving nonlocal conditions. Using the theory of resolvent operators, some fixed point theorems, and an estimation technique of Kuratowski measure of noncompactness, we first establish some existence results of mild solutions for the proposed equation. Subsequently, we show by applying a newly established lemma that these solutions have regularity property under some conditions. Finally, as a sample of application, the obtained results are applied to a class of non-autonomous nonlocal partial integrodifferential equations.Threshold dynamics of a vector-bias malaria model with time-varying delays in environments of almost periodicityhttps://zbmath.org/1544.341502024-11-01T15:51:55.949586Z"He, Bing"https://zbmath.org/authors/?q=ai:he.bing.1"Wang, Qi-Ru"https://zbmath.org/authors/?q=ai:wang.qiruSummary: A malaria transmission model having vector bias and time-dependent delays in environments of almost periodicity is considered. The basic reproduction ratio \(\mathcal{R}_0\) is presented, and the threshold dynamic is characterized by \(\mathcal{R}_0\). By using the theories of skew-product semiflows, chain transitive sets, and subhomogeneous and monotone systems, it is proved that the model has only one positive almost periodic solution with global asymptotic stability provided \(\mathcal{R}_0 > 1\), and the almost periodic (disease-free) solution has global asymptotic stability provided \(\mathcal{R}_0 < 1\). In addition, some numerical simulations are given.Lie symmetry analysis, particular solutions and conservation laws for the dissipative (2+1)-dimensional AKNS equationhttps://zbmath.org/1544.350182024-11-01T15:51:55.949586Z"Tao, Sixing"https://zbmath.org/authors/?q=ai:tao.sixing(no abstract)Subgroups of Lie groups and symmetry reduction for nonlinear partial differential equationshttps://zbmath.org/1544.350192024-11-01T15:51:55.949586Z"Grundland, A. M."https://zbmath.org/authors/?q=ai:grundland.alfred-michel"Harnad, J."https://zbmath.org/authors/?q=ai:harnad.john"Winternitz, P."https://zbmath.org/authors/?q=ai:winternitz.pavelSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].The associated Lie algebra of \(\ddot x+f_2\dot x+f_1x=f_0\)https://zbmath.org/1544.350202024-11-01T15:51:55.949586Z"Krause, J."https://zbmath.org/authors/?q=ai:krause.jurgen|krause.jorg|krause.jens|krause.jochen|krause.jorge|krause.james-m|krause.joscha"Aguirre, M."https://zbmath.org/authors/?q=ai:aguirre.miguel-a|aguirre.m-c|aguirre.miquel|aguirre.manuel-aSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].Potentialisations of a class of fully-nonlinear symmetry-integrable evolution equationshttps://zbmath.org/1544.350222024-11-01T15:51:55.949586Z"Euler, Marianna"https://zbmath.org/authors/?q=ai:euler.marianna"Euler, Norbert"https://zbmath.org/authors/?q=ai:euler.norbertSummary: We consider here the class of fully-nonlinear symmetry-integrable third-order evolution equations in 1+1 dimensions that were proposed recently by us [Open Commun. Nonlinear Math. Phys. 2, 216--228 (2022; Zbl 1544.35021)]. In particular, we report all zero-order and higher-order potentialisations for this class of equations using their integrating factors (or multipliers) up to order four. Chains of connecting evolution equations are also obtained by multi-potentialisations.A Lipschitz metric for \(\alpha\)-dissipative solutions to the Hunter-Saxton equationhttps://zbmath.org/1544.350322024-11-01T15:51:55.949586Z"Grunert, Katrin"https://zbmath.org/authors/?q=ai:grunert.katrin"Tandy, Matthew"https://zbmath.org/authors/?q=ai:tandy.matthewSummary: We explore the Lipschitz stability of solutions to the Hunter-Saxton equation with respect to the initial data. In particular, we study the stability of \(\alpha\)-dissipative solutions constructed using a generalised method of characteristics approach, where \(\alpha\) is a function determining the energy loss at each position in space.On growth and instability for semilinear evolution equations: an abstract approachhttps://zbmath.org/1544.350512024-11-01T15:51:55.949586Z"Müller, Vladimir"https://zbmath.org/authors/?q=ai:muller.vladimir"Schnaubelt, Roland"https://zbmath.org/authors/?q=ai:schnaubelt.roland"Tomilov, Yuri"https://zbmath.org/authors/?q=ai:tomilov.yuriSummary: We propose a new approach to the study of (nonlinear) growth and instability for semilinear abstract evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of linear evolution equations can be treated as linear ones as far as the growth of their solutions is concerned. We obtain exponential lower bounds of solutions for initial values from a dense set in resolvent or spectral terms. The abstract results are applied, in particular, to the study of energy growth for semilinear backward damped wave equations.Dynamics for wave equations connected in parallel with nonlinear localized dampinghttps://zbmath.org/1544.350552024-11-01T15:51:55.949586Z"Gao, Yunlong"https://zbmath.org/authors/?q=ai:gao.yunlong"Sun, Chunyou"https://zbmath.org/authors/?q=ai:sun.chunyou"Zhang, Kaibin"https://zbmath.org/authors/?q=ai:zhang.kaibinSummary: This study investigates the properties of solutions about one-dimensional wave equations connected in parallel under the effect of two nonlinear localized frictional damping mechanisms. First, under various growth conditions about the nonlinear dissipative effect, we try to establish the decay rate estimates by imposing minimal amount of support on the damping and provide some examples of exponential decay and polynomial decay. To achieve this, a proper observability inequality has been proposed and constructed based on some refined microlocal analysis. Then, the existence of a global attractor is proved when the damping terms are linearly bounded at infinity, a special weighting function has been used in this part, which eliminates undesirable terms of the higher order while contributing lower-order terms. Finally, we establish that the long-time behavior of solutions of the nonlinear system is completely determined by the dynamics of large finite number of functionals.Existence of periodic waves in a perturbed generalized BBM equationhttps://zbmath.org/1544.350842024-11-01T15:51:55.949586Z"Dai, Yanfei"https://zbmath.org/authors/?q=ai:dai.yanfei"Wei, Minzhi"https://zbmath.org/authors/?q=ai:wei.minzhi"Han, Maoan"https://zbmath.org/authors/?q=ai:han.maoan(no abstract)Nonstandard solutions for a perturbed nonlinear Schrödinger system with small coupling coefficientshttps://zbmath.org/1544.350882024-11-01T15:51:55.949586Z"An, Xiaoming"https://zbmath.org/authors/?q=ai:an.xiaoming"Wang, Chunhua"https://zbmath.org/authors/?q=ai:wang.chunhua.1This paper deals with ``the following weakly coupled nonlinear Schrödinger system
\[
\left\{ \begin{array}{ll} -\epsilon^2\Delta u_1 + V_1(x)u_1 = |u_1|^{2p-2}u_1 + \beta |u_1|^{p-2}|u_2|^pu_1, & x\in\mathbb{R}^N \\
-\epsilon^2\Delta u_2 + V_2(x)u_2 = |u_2|^{2p-2}u_2 + \beta |u_2|^{p-2}|u_1|^pu_2, & x\in\mathbb{R}^N \end{array} \right.
\]
where \(\epsilon>0\), \(\beta\in\mathbb{R}\) is a coupling constant, \(2p\in (2,2^*)\) with \(2^* = \frac{2N}{N - 2}\) if \(N\geq 3\) and \(+\infty\) if \(N = 1,2\), \(V_1\) and \(V_2\) belong to \(C(\mathbb{R}^N,[0,\infty))\).''
When \(p\ge 2\) and \(|\beta|<\beta_0\) for some positive constant \(\beta_0>0\), By using variational methods and the penalized technique, the paper shows that the problem has a family of nonstandard solutions \(\{w_{\epsilon} = (u^1_{\epsilon},u^2_{\epsilon}):0<\epsilon<\epsilon_{0}\}\) concentrating synchronously at the common local minimum of \(V_1\) and \(V_2\). All decay rates of \(V_i(i=1,2)\) especiallly the compactly supported case are included. Due to the loss of monotonicity of higher energy, the peak is located by the local Pohozaev identity instead of the usual energy comparison. Moreover, a type of concentration-compactness principle in weakly coupled nonlinear Schrödinger systems is established to ensure the nontrivial properties of both sectors of \(w_\epsilon\) (\(\lim_{\varepsilon>0}\|u^i_\epsilon\|_{L^{\infty}(\mathbb{R}^N)}>0,i=1,2\)).
Reviewer: Shuangjie Peng (Wuhan)Amplitude equations for wave bifurcations in reaction-diffusion systemshttps://zbmath.org/1544.351002024-11-01T15:51:55.949586Z"Villar-Sepúlveda, Edgardo"https://zbmath.org/authors/?q=ai:villar-sepulveda.edgardo"Champneys, Alan"https://zbmath.org/authors/?q=ai:champneys.alan-rSummary: A wave bifurcation is the counterpart to a Turing instability in reaction-diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. Such bifurcations require at least three components and give rise to patterns that are periodic in both space and time. Depending on boundary conditions, these patterns can comprise either rotating or standing waves. Restricting to systems in one spatial dimension, complete formulae are derived for the evaluation of the coefficients of the weakly nonlinear normal form of the bifurcation up to order five, including those that determine the criticality of both rotating and standing waves. The formulae apply to arbitrary \(n\)-component systems \((n\geqslant 3)\) and their evaluation is implemented in software which is made available as supplementary material. The theory is illustrated on two different versions of three-component reaction-diffusion models of excitable media that were previously shown to feature super- and subcritical wave instabilities and on a five-component model of two-layer chemical reaction. In each case, two-parameter bifurcation diagrams are produced to illustrate the connection between complex dispersion relations and different types of Hopf, Turing, and wave bifurcations, including the existence of several codimension-two bifurcations.
{{\copyright} 2024 The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society}Bifurcations and exact bounded solutions of some traveling wave systems determined by integrable nonlinear oscillators with \(q\)-degree dampinghttps://zbmath.org/1544.351012024-11-01T15:51:55.949586Z"Zhang, Lijun"https://zbmath.org/authors/?q=ai:zhang.lijun.2"Chen, Guanrong"https://zbmath.org/authors/?q=ai:chen.guanrong"Li, Jibin"https://zbmath.org/authors/?q=ai:li.jibin(no abstract)Global population propagation dynamics of reaction-diffusion models with shifting environment for non-monotone kinetics and birth pulsehttps://zbmath.org/1544.351022024-11-01T15:51:55.949586Z"Zhang, Yurong"https://zbmath.org/authors/?q=ai:zhang.yurong"Yi, Taishan"https://zbmath.org/authors/?q=ai:yi.taishan"Wu, Jianhong"https://zbmath.org/authors/?q=ai:wu.jianhongSummary: We consider a general impulsive reaction-diffusion equation with shifting environment and birth pulse, both induced by climate changes, to capture essential features of the dynamics of species exhibiting distinct stages of reproduction and dispersal. We convert this model into a discrete-time semiflow, and hence to a discrete-time recursion system. We establish the existence of forced waves and asymptotic spreading properties of solutions, and obtain sufficient conditions for the global asymptotic stability of the forced waves.An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimensionhttps://zbmath.org/1544.351042024-11-01T15:51:55.949586Z"Lappicy, Phillipo"https://zbmath.org/authors/?q=ai:lappicy.phillipo"Beatriz, Ester"https://zbmath.org/authors/?q=ai:beatriz.esterSummary: Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for quasilinear non-degenerate parabolic equations. We modify Matano's method to construct an energy formula for fully nonlinear degenerate parabolic equations. We provide several examples of formulae, and in particular, a new energy candidate for the porous medium equation.N-soliton solutions for the three-component Dirac-Manakov system via Riemann-Hilbert approachhttps://zbmath.org/1544.351142024-11-01T15:51:55.949586Z"Wang, Yuxia"https://zbmath.org/authors/?q=ai:wang.yuxia"Huang, Lin"https://zbmath.org/authors/?q=ai:huang.lin.3|huang.lin|huang.lin.1"Yu, Jing"https://zbmath.org/authors/?q=ai:yu.jing.1|yu.jingSummary: This investigation delves into the application of the well-established Riemann-Hilbert method for the elucidation of the N-solitons solution of the three-component Dirac-Manakov system. The analytical process is structured in two fundamental steps. Initially, the inverse scattering method is employed to establish a pivotal connection between the solution of the three-component DiracManakov system and the associated Riemann-Hilbert problem. Subsequently, we systematically address the resolution of this pertinent Riemann-Hilbert problem. Through the assignment of specific values to the relevant parameters in our solution, we adeptly generate graphical representations that vividly illustrate the nuanced dynamics inherent in the solution of the three-component DiracManakov system.Higher-dimensional integrable deformations of the classical Boussinesq-Burgers systemhttps://zbmath.org/1544.351332024-11-01T15:51:55.949586Z"Cheng, Xiaoyu"https://zbmath.org/authors/?q=ai:cheng.xiaoyu"Huang, Qing"https://zbmath.org/authors/?q=ai:huang.qing(no abstract)Decomposition solutions and Bäcklund transformations of the B-type and C-type Kadomtsev-Petviashvili equationshttps://zbmath.org/1544.351342024-11-01T15:51:55.949586Z"Hao, Xiazhi"https://zbmath.org/authors/?q=ai:hao.xiazhi"Lou, S. Y."https://zbmath.org/authors/?q=ai:lou.senyue(no abstract)Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equationhttps://zbmath.org/1544.351352024-11-01T15:51:55.949586Z"Jiang, DongZhu"https://zbmath.org/authors/?q=ai:jiang.dongzhu"Zhaqilao"https://zbmath.org/authors/?q=ai:zhaqilao.z(no abstract)New patterns of localized excitations in (2+1)-dimensions: the fifth-order asymmetric Nizhnik-Novikov-Veselov equationhttps://zbmath.org/1544.351392024-11-01T15:51:55.949586Z"Wang, Jianyong"https://zbmath.org/authors/?q=ai:wang.jianyong"Chai, Yuanhua"https://zbmath.org/authors/?q=ai:chai.yuanhua(no abstract)Rogue waves for the (2+1)-dimensional Myrzakulov-Lakshmanan-IV equation on a periodic backgroundhttps://zbmath.org/1544.351402024-11-01T15:51:55.949586Z"Wang, Xiao-Hui"https://zbmath.org/authors/?q=ai:wang.xiaohui"Zhaqilao"https://zbmath.org/authors/?q=ai:zhaqilao.z(no abstract)The Mumford dynamical system and the Gelfand-Dikii recursionhttps://zbmath.org/1544.351422024-11-01T15:51:55.949586Z"Baron, P. G."https://zbmath.org/authors/?q=ai:baron.p-gIt is difficult to present the contents of this paper, so I simply reproduce below the abstract of the paper which might be useful for interested people.
In his paper [Funct. Anal. Appl. 57, No. 4, 288--302 (2023; Zbl 1540.35336); translation from Funkts. Anal. Prilozh. 57, No. 4, 27--45 (2023)], \textit{V. M. Buchstaber} developed the differential-algebraic theory of the Mumford dynamical system. The key object of this theory is the (P, Q)-recursion introduced in his paper. In the present paper, we further develop the theory of the (P, Q)-recursion and describe its connections to the Korteweg-de Vries hierarchy, the Lenard operator, and the Gelfand-Dikii recursion.
Reviewer: Gheorghe Moroşanu (Cluj-Napoca)Ren-integrable and Ren-symmetric integrable systemshttps://zbmath.org/1544.351452024-11-01T15:51:55.949586Z"Lou, S. Y."https://zbmath.org/authors/?q=ai:lou.senyue(no abstract)Traveling wave solution of the Olver-Rosenau equation solved by dynamics systemhttps://zbmath.org/1544.351482024-11-01T15:51:55.949586Z"Xiong, Mei"https://zbmath.org/authors/?q=ai:xiong.mei"Chen, Longwei"https://zbmath.org/authors/?q=ai:chen.longwei"Yang, Na"https://zbmath.org/authors/?q=ai:yang.naSummary: Olver-Rosenau equations presented by Olver and Rosenau can be rewritten to the dynamic system by the wave transformation. The system is a Hamiltonian system with the first integral, and its phase-space and equilibrium point analysis are given in different parameter spaces in detail. On this basis, we can derive various solutions of the original equation relating these orbits in different phase-space planes, and the theoretical basis of the numerical solution is provided for engineering application and production practice.Mass-energy threshold dynamics for the focusing NLS with a repulsive inverse-power potentialhttps://zbmath.org/1544.351502024-11-01T15:51:55.949586Z"Ardila, Alex H."https://zbmath.org/authors/?q=ai:ardila.alex-hernandez"Hamano, Masaru"https://zbmath.org/authors/?q=ai:hamano.masaru"Ikeda, Masahiro"https://zbmath.org/authors/?q=ai:ikeda.masahiroSummary: In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exactly at the mass-energy threshold, namely, when \(E_V (u_0) M(u_0) = E_0 (Q)M(Q)\). Moreover, we prove failure of the uniform space-time bounds at the mass-energy threshold.Focusing nonlocal nonlinear Schrödinger equation with asymmetric boundary conditions: large-time behaviorhttps://zbmath.org/1544.351532024-11-01T15:51:55.949586Z"Boutet de Monvel, Anne"https://zbmath.org/authors/?q=ai:boutet-de-monvel.anne-marie"Rybalko, Yan"https://zbmath.org/authors/?q=ai:rybalko.yan"Shepelsky, Dmitry"https://zbmath.org/authors/?q=ai:shepelskyi.dmytro-georgiiovychThe purpose of this paper is to study the initial value problem for the focusing nonlocal nonlinear Schrödinger equation
\[
\begin{cases}
iu_{t}\left( x,t\right) +u_{xx}\left( x,t\right) +2u^{2}\left(x,t\right) \overline{u\left( -x,t\right) }=0,\ x\in\mathbb{R}\ t\in\mathbb{R},\\
u\left( x,0\right) =u_{0}\left( x\right),\ x\in\mathbb{R},
\end{cases} \tag{1}
\]
(\(\overline{u}\) denotes the complex conjugate of \(u\)) with asymmetric nonzero boundary conditions:
\[
u\left( x,t\right) \rightarrow\pm Ae^{-2iA^{2}t},\quad x\rightarrow\pm\infty,\ t\in\mathbb{R}.
\]
It is shown that for a class of initial data there exist three qualitatively different asymptotic zones in the \(\left( x,t\right)\) plane: the regions \(\left\vert \frac{x}{4t}\right\vert \in\left( A/2,\infty\right),\) where the parameters are modulated, i.e., they depend on the ratio \(\frac{x}{t},\) and a central region \(\left\vert \frac{x}{4t}\right\vert \in\left( 0,A/2\right)\), where the parameters are unmodulated. The asymptotics of the solution as \(\xi\rightarrow\pm0\), for fixed \(x=x_{0}>0\) and \(t\rightarrow\infty\) is also considered. The method used in this paper is based on the inverse scattering transform, that allows to express the solution of problem (1) in terms of the solution of an associated Riemann-Hilbert problem, and the Deift and Zhou nonlinear steepest descent method in [\textit{P. A. Deift} et al., in: Important developments in soliton theory. Berlin: Springer-Verlag. 181--204 (1993; Zbl 0926.35132); \textit{P. Deift} and \textit{X. Zhou}, Ann. Math. (2) 137, No. 2, 295--368 (1993; Zbl 0771.35042)].
For the entire collection see [Zbl 1519.47002].
Reviewer: Ivan Naumkin (Ciudad de México)A general coupled derivative nonlinear Schrödinger system: Darboux transformation and soliton solutionshttps://zbmath.org/1544.351552024-11-01T15:51:55.949586Z"Kuang, Yonghui"https://zbmath.org/authors/?q=ai:kuang.yonghuiSummary: In this work we present a general coupled derivative nonlinear Schrödinger system. We construct the corresponding \(N\)-fold Darboux transform and generalized Darboux transform. Under this construction, we give different soliton solutions and plot their figures describing the soliton characteristics and dynamical behaviors, including higher-order soliton and rouge wave solution etc.Deformation of optical solitons in a variable-coefficient nonlinear Schrödinger equation with three distinct \(\mathcal{PT}\)-symmetric potentials and modulated nonlinearitieshttps://zbmath.org/1544.351562024-11-01T15:51:55.949586Z"Manikandan, K."https://zbmath.org/authors/?q=ai:manikandan.kannan"Sakkaravarthi, K."https://zbmath.org/authors/?q=ai:sakkaravarthi.k"Sudharsan, J. B."https://zbmath.org/authors/?q=ai:sudharsan.j-b"Aravinthan, D."https://zbmath.org/authors/?q=ai:aravinthan.d(no abstract)Binary Darboux transformation of vector nonlocal reverse-space nonlinear Schrödinger equationshttps://zbmath.org/1544.351572024-11-01T15:51:55.949586Z"Ma, Wen-Xiu"https://zbmath.org/authors/?q=ai:ma.wen-xiu"Huang, Yehui"https://zbmath.org/authors/?q=ai:huang.yehui"Wang, Fudong"https://zbmath.org/authors/?q=ai:wang.fudong"Zhang, Yong"https://zbmath.org/authors/?q=ai:zhang.yong.18|zhang.yong|zhang.yong.54|zhang.yong.2|zhang.yong.13|zhang.yong.12|zhang.yong.9|zhang.yong.41|zhang.yong.62|zhang.yong.67|zhang.yong.10|zhang.yong.8|zhang.yong.28|zhang.yong.59|zhang.yong.15|zhang.yong.5|zhang.yong.52|zhang.yong.57|zhang.yong.60|zhang.yong.64|zhang.yong.14|zhang.yong.19|zhang.yong.4"Ding, Liyuan"https://zbmath.org/authors/?q=ai:ding.liyuanSummary: For vector nonlocal reverse-space nonlinear Schrödinger equations, a binary Darboux transformation is formulated by using two sets of eigenfunctions and adjoint eigenfunctions. The resulting binary Darboux transformation has been decomposed into an \(N\)-fold product of single binary Darboux transformations. An application starting from zero seed potentials generates a class of soliton solutions.Stability of black solitons in optical systems with intensity-dependent dispersionhttps://zbmath.org/1544.351592024-11-01T15:51:55.949586Z"Pelinovsky, Dmitry E."https://zbmath.org/authors/?q=ai:pelinovsky.dmitry-e"Plum, Michael"https://zbmath.org/authors/?q=ai:plum.michaelAuthors' abstract: Black solitons are identical in the nonlinear Schrödinger (NLS) equation with intensity-dependent dispersion and the cubic defocusing NLS equation. We prove that the intensity-dependent dispersion introduces new properties in the stability analysis of the black soliton. First, the spectral stability problem possesses only isolated eigenvalues on the imaginary axis. Second, the energetic stability argument holds in Sobolev spaces with exponential weights. Third, the black soliton persists with respect to the addition of a small decaying potential and remains spectrally stable when it is pinned to the minimum points of the effective potential. The same model exhibits a family of traveling dark solitons for every wave speed and we incorporate properties of these dark solitons for small wave speeds in the analysis of orbital stability of the black soliton.
Reviewer: Alessandro Selvitella (Fort Wayne)The quasi-Gramian solution of a non-commutative extension of the higher-order nonlinear Schrödinger equationhttps://zbmath.org/1544.351602024-11-01T15:51:55.949586Z"Riaz, H. W. A."https://zbmath.org/authors/?q=ai:riaz.h-wajahat-ahmed.2"Lin, J."https://zbmath.org/authors/?q=ai:lin.ji.1(no abstract)Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equationshttps://zbmath.org/1544.351622024-11-01T15:51:55.949586Z"Tefera, Alemu Yilma"https://zbmath.org/authors/?q=ai:tefera.alemu-yilma"Li, Shangshuai"https://zbmath.org/authors/?q=ai:li.shangshuai"Zhang, Da-jun"https://zbmath.org/authors/?q=ai:zhang.dajun(no abstract)Beyond-band discrete soliton interaction in binary waveguide arrayshttps://zbmath.org/1544.351632024-11-01T15:51:55.949586Z"Tran, Minh C."https://zbmath.org/authors/?q=ai:tran.minh-cong"Tran, Truong X."https://zbmath.org/authors/?q=ai:tran.truong-x(no abstract)The exact solutions for the non-isospectral Kaup-Newell hierarchy via the inverse scattering transformhttps://zbmath.org/1544.351642024-11-01T15:51:55.949586Z"Zhang, Hongyi"https://zbmath.org/authors/?q=ai:zhang.hongyi"Zhang, Yufeng"https://zbmath.org/authors/?q=ai:zhang.yu-feng"Feng, Binlu"https://zbmath.org/authors/?q=ai:feng.binlu"Afzal, Faiza"https://zbmath.org/authors/?q=ai:afzal.faizaSummary: We begin by introducing a non-isospectral Lax pair, from which we derive a non-isospectral integrable Kaup-Newell hierarchy. The new general solutions for the non-isospectral integrable Kaup-Newell hierarchy are obtained through the inverse scattering transform (IST) method. Finally, we obtain the soliton solutions of a reduced non-isospectral integrable equation from non-isospectral integrable Kaup-Newell hierarchy. For 1-soliton solution, we obtain the explicit expression and analyze the dynamical behavior of soliton solution; for 2-soliton solutions, we verify that collisions between soliton solutions are inelastic collisions. The significant difference of the paper from the works finished by other authors (such as
[\textit{T.-k. Ning} et al., Chaos Solitons Fractals 21, No. 2, 395--401 (2004; Zbl 1049.35160);
Physica A 339, 248--266 (2004; \url{doi:10.1016/j.physa.2004.03.021});
\textit{Q. Li} et al., J. Phys. A, Math. Theor. 41, No. 35, Article ID 355209, 14 p. (2008; Zbl 1158.35418);
Commun. Theor. Phys. 54, No. 2, 219--228 (2010; Zbl 1219.35240);
Chaos Solitons Fractals 45, No. 12, 1479--1485 (2012; Zbl 1258.37066)]) lies in except for the spectral parameter \(\lambda\) being higher order, not one-order of \(\lambda\).A KdV-SIR equation and its analytical solutions for solitary epidemic waveshttps://zbmath.org/1544.351772024-11-01T15:51:55.949586Z"Paxson, Wei"https://zbmath.org/authors/?q=ai:paxson.wei"Shen, Bo-Wen"https://zbmath.org/authors/?q=ai:shen.bo-wen(no abstract)General solution of the singular fractional Fornasini-Marchesini linear systemshttps://zbmath.org/1544.351852024-11-01T15:51:55.949586Z"Benyettou, Kamel"https://zbmath.org/authors/?q=ai:benyettou.kamel"Ghezzar, Mohammed Amine"https://zbmath.org/authors/?q=ai:ghezzar.mohammed-amine"Bouagada, Djillali"https://zbmath.org/authors/?q=ai:bouagada.djillaliSummary: The purpose of this research is to compute the solution of two dimensional singular systems expressed by Fornasini-Marchesini models. A new result using some 2D transforms is given. The goal of this study is to discuss the applicability of the fundamental matrix and delta Kronecker to solve this class of system. The derived results are then compared with the existing the solution formula for the standard models. All the obtained study results are expressed numerically to demonstrate the validity and effectiveness of the proposed method.Determination of unknown time-dependent heat source in inverse problems under nonlocal boundary conditions by finite integration methodhttps://zbmath.org/1544.352082024-11-01T15:51:55.949586Z"Hazanee, Areena"https://zbmath.org/authors/?q=ai:hazanee.areena"Makaje, Nifatamah"https://zbmath.org/authors/?q=ai:makaje.nifatamahSummary: In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.The mathematics of cellular automatahttps://zbmath.org/1544.370012024-11-01T15:51:55.949586Z"Hawkins, Jane"https://zbmath.org/authors/?q=ai:hawkins.jane-mCellular automata are discrete models of organisms: arrays of cells, each evolving according to the same pre-established rule and depending on the cell's internal state as well as on the states of its immediate neighbours. As such, they are a fundamental model of how complexity may emerge from very simple building blocks.
The book under review introduces some of the main features and properties of cellular automata, from a mathematical viewpoint. It should not be treated as a reference (though it does make pleasant reading), but rather as the support of an introductory course on cellular automata, introducing basic mathematical concepts along the way.
In fact, I believe the reverse is also true: {it is a course on basic mathematics (calculus), motivated by cellular automata as a running example.} In particular, the reader will learn about metric spaces, (equi)continuity, etc. The text contains proofs of the main results, often richly illustrated via cellular automata.
A few caveats for the professional mathematician: the results presented in this book heavily focus on one-dimensional cellular automata, those for which the cells are arranged in a linear array. There is a single chapter on two-dimensional cellular automata, focussing on Conway's ``game of life'', and the celebrated Moore-Myhill theorems, while valid in arbitrary-dimensional grids, are only proven in dimension one. As such, the beautiful connection between \((d+1)\)-dimensional tiling problems and \(d\)-dimensional cellular automata is missing.
For a mathematically more thorough treatment, I would recommend \textit{T. Ceccherini-Silberstein} and \textit{M. Coornaert}'s [Cellular automata and groups. 2nd edition. Cham: Springer (2023; Zbl 1531.37003)].
Reviewer: Laurent Bartholdi (Saarbrücken)Homotopical dynamics for gradient-like flows. Lecture notes from the 34th Brazilian mathematics colloquium -- 34\degree Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro, Brazil, Juli 2023https://zbmath.org/1544.370022024-11-01T15:51:55.949586Z"Ledesma, Guido G. E."https://zbmath.org/authors/?q=ai:ledesma.guido-g-e"Lima, Dahisy V. S."https://zbmath.org/authors/?q=ai:lima.dahisy-valadao-de-souza"Mello, Margarida P."https://zbmath.org/authors/?q=ai:mello.margarida-pinheiro"de Rezende, Ketty A."https://zbmath.org/authors/?q=ai:de-rezende.ketty-abaroa"da Silveira, Mariana R."https://zbmath.org/authors/?q=ai:da-silveira.mariana-r(no abstract)Framework for global stability analysis of dynamical systemshttps://zbmath.org/1544.370032024-11-01T15:51:55.949586Z"Datseris, George"https://zbmath.org/authors/?q=ai:datseris.george"Rossi, Kalel Luiz"https://zbmath.org/authors/?q=ai:rossi.kalel-luiz"Wagemakers, Alexandre"https://zbmath.org/authors/?q=ai:wagemakers.alexandre(no abstract)Drift of random walks on abelian covers of finite volume homogeneous spaceshttps://zbmath.org/1544.370042024-11-01T15:51:55.949586Z"Bénard, Timothée"https://zbmath.org/authors/?q=ai:benard.timotheeAuthor's abstract: Let \(G\) be a connected simple real Lie group, \( \Lambda_{0} \subseteq G\) a lattice without torsion and \(\Lambda \unlhd \Lambda_{0}\) a normal subgroup such that \(\Lambda_{0} /\Lambda \simeq \mathbb{Z}^{d}\). We study the drift of a random walk on the \(\mathbb{Z}^{d}\)-cover \(\Lambda \setminus G\) of the finite volume homogeneous space \(\Lambda_{0} \setminus G\). This walk is defined by a Zariski-dense compactly supported probability measure \(\mu\) on \(G\). We first assume the covering map \(\Lambda \setminus G \rightarrow \Lambda_{0} \setminus G\) does not unfold any cusp of \(\Lambda_{0} \setminus G\) and compute the drift at every starting point. Then we remove this assumption and describe the drift almost everywhere. The case of hyperbolic manifolds of dimension \(2\) stands out with non-converging type behaviors. The recurrence of the trajectories is also characterized in this context.
Reviewer: V. V. Gorbatsevich (Moskva)Existence of the zero-temperature limit of equilibrium states on topologically transitive countable Markov shiftshttps://zbmath.org/1544.370052024-11-01T15:51:55.949586Z"Beltrán, Elmer"https://zbmath.org/authors/?q=ai:beltran.elmer-r"Littin, Jorge"https://zbmath.org/authors/?q=ai:littin.jorge-c"Maldonado, Cesar"https://zbmath.org/authors/?q=ai:maldonado.cesar"Vargas, Victor"https://zbmath.org/authors/?q=ai:vargas.victorSummary: Consider a topologically transitive countable Markov shift \(\Sigma\) and a summable locally constant potential \(\phi\) with finite Gurevich pressure and \(\mathrm{Var}_1(\phi)<\infty\). We prove the existence of the limit \(\lim_{t\to\infty}\mu_t\) in the weak\(^\star\) topology, where \(\mu_t\) is the unique equilibrium state associated to the potential \(t\phi\). In addition, we present examples where the limit at zero temperature exists for potentials satisfying more general conditions.Minimal subdynamics and minimal flows without characteristic measureshttps://zbmath.org/1544.370062024-11-01T15:51:55.949586Z"Frisch, Joshua"https://zbmath.org/authors/?q=ai:frisch.joshua-r"Seward, Brandon"https://zbmath.org/authors/?q=ai:seward.brandon-m"Zucker, Andy"https://zbmath.org/authors/?q=ai:zucker.andySummary: Given a countable group \(G\) and a \(G\)-flow \(X\), a probability measure \(\mu\) on \(X\) is called characteristic if it is \(\text{Aut}(X, G)\)-invariant. \textit{J. Frisch} and \textit{O. Tamuz} [Ergodic Theory Dyn. Syst. 42, No. 5, 1655--1661 (2022; Zbl 1501.37014)] asked about the existence of a minimal \(G\)-flow, for any group \(G\), which does not admit a characteristic measure. We construct for every countable group \(G\) such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group \(G\) and a collection of infinite subgroups \(\{\Delta_i: i\in I\}\), when is there a faithful \(G\)-flow for which every \(\Delta_i\) acts minimally?Isometric actions are quasidiagonalhttps://zbmath.org/1544.370072024-11-01T15:51:55.949586Z"Pilgrim, Samantha"https://zbmath.org/authors/?q=ai:pilgrim.samanthaSummary: We show every isometric action of a countable discrete group on a compact space is quasidiagonal in a strong sense. This shows that reduced crossed products by such actions are quasidiagonal or MF whenever the reduced group \(C^*\)-algebra of the acting group is quasidiagonal or MF. We use this to show new examples of group actions whose crossed products are MF.A review of symbolic dynamics and symbolic reconstruction of dynamical systemshttps://zbmath.org/1544.370082024-11-01T15:51:55.949586Z"Hirata, Yoshito"https://zbmath.org/authors/?q=ai:hirata.yoshito"Amigó, José M."https://zbmath.org/authors/?q=ai:amigo.jose-maria(no abstract)Irreversibility of 2D linear CA and Garden of Edenhttps://zbmath.org/1544.370092024-11-01T15:51:55.949586Z"Jumaniyozov, Doston"https://zbmath.org/authors/?q=ai:jumaniyozov.doston"Omirov, Bakhrom"https://zbmath.org/authors/?q=ai:omirov.bakhrom-a"Redjepov, Shovkat"https://zbmath.org/authors/?q=ai:redjepov.shovkat"Uguz, Selman"https://zbmath.org/authors/?q=ai:uguz.selman(no abstract)Complexity of generic limit sets of cellular automatahttps://zbmath.org/1544.370102024-11-01T15:51:55.949586Z"Törmä, Ilkka"https://zbmath.org/authors/?q=ai:torma.ilkka-aSummary: The generic limit set of a topological dynamical system is the smallest closed subset of the phase space that has a comeager realm of attraction. It intuitively captures the asymptotic dynamics of almost all initial conditions. It was defined by \textit{J. Milnor} [Commun. Math. Phys. 99, 177--195 (1985; Zbl 0595.58028)]
and studied in the context of cellular automata, whose generic limit sets are subshifts, by \textit{S. Djenaoui} and \textit{P. Guillon} [J. Cell. Autom. 14, No. 5--6, 435--477 (2019; Zbl 1478.37023)]. In this article we study the structural and computational restrictions that apply to generic limit sets of cellular automata. As our main result, we show that the language of a generic limit set can be at most \(\varSigma^0_3\)-hard, and lower in various special cases. We also prove a structural restriction on generic limit sets with a global period.
For the entire collection see [Zbl 1464.68024].Recurrence plots bridge deterministic systems and stochastic systems topologically and measure-theoreticallyhttps://zbmath.org/1544.370112024-11-01T15:51:55.949586Z"Hirata, Yoshito"https://zbmath.org/authors/?q=ai:hirata.yoshito"Shiro, Masanori"https://zbmath.org/authors/?q=ai:shiro.masanori(no abstract)Transitivity and shadowing properties of nonautonomous discrete dynamical systemshttps://zbmath.org/1544.370122024-11-01T15:51:55.949586Z"Pi, Jingmin"https://zbmath.org/authors/?q=ai:pi.jingmin"Lu, Tianxiu"https://zbmath.org/authors/?q=ai:lu.tianxiu"Xue, Yanfu"https://zbmath.org/authors/?q=ai:xue.yanfu(no abstract)An ``observable'' horseshoe maphttps://zbmath.org/1544.370132024-11-01T15:51:55.949586Z"Zhang, Xu"https://zbmath.org/authors/?q=ai:zhang.xu"Wang, Yukai"https://zbmath.org/authors/?q=ai:wang.yukai"Chen, Guanrong"https://zbmath.org/authors/?q=ai:chen.guanrong(no abstract)Heteroclinic connections for nonlocal equationshttps://zbmath.org/1544.370142024-11-01T15:51:55.949586Z"Dipierro, Serena"https://zbmath.org/authors/?q=ai:dipierro.serena"Patrizi, Stefania"https://zbmath.org/authors/?q=ai:patrizi.stefania"Valdinoci, Enrico"https://zbmath.org/authors/?q=ai:valdinoci.enricoSummary: We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a renormalized energy functional, exploits a perturbation method of viscosity type, combined with an auxiliary penalization method, and develops a free boundary theory for a double obstacle problem of mixed local and nonlocal type. The description of the stationary positions for the atom dislocation function in a perturbed crystal, as given by the Peierls-Nabarro model, is a particular case of the result presented.Persistence of heterodimensional cycleshttps://zbmath.org/1544.370152024-11-01T15:51:55.949586Z"Li, Dongchen"https://zbmath.org/authors/?q=ai:li.dongchen"Turaev, Dmitry"https://zbmath.org/authors/?q=ai:turaev.dmitry-vSummary: A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of orbits that connect them. For systems which are at least \(C^2\), we show that bifurcations of a coindex-1 heterodimensional cycle within a generic 2-parameter family create robust heterodimensional dynamics, i.e., a pair of non-trivial hyperbolic basic sets with different numbers of positive Lyapunov exponents, such that the unstable manifold of each of the sets intersects the stable manifold of the second set and these intersections persist for an open set of parameter values. We also give a solution to the so-called local stabilization problem of coindex-1 heterodimensional cycles in any regularity class \(r=2, \dots, \infty, \omega\). The results are based on the observation that arithmetic properties of moduli of topological conjugacy of systems with heterodimensional cycles determine the emergence of Bonatti-Díaz blenders.Singularly degenerate heteroclinic cycles with nearby apple-shape attractorshttps://zbmath.org/1544.370162024-11-01T15:51:55.949586Z"Wang, Haijun"https://zbmath.org/authors/?q=ai:wang.haijun.1"Ke, Guiyao"https://zbmath.org/authors/?q=ai:ke.guiyao"Dong, Guili"https://zbmath.org/authors/?q=ai:dong.guili"Su, Qifang"https://zbmath.org/authors/?q=ai:su.qifang"Pan, Jun"https://zbmath.org/authors/?q=ai:pan.jun(no abstract)Limit theorems for self-intersecting trajectories in \(\mathbb{Z}\)-extensionshttps://zbmath.org/1544.370172024-11-01T15:51:55.949586Z"Phalempin, Maxence"https://zbmath.org/authors/?q=ai:phalempin.maxenceSummary: We investigate the asymptotic properties of the self-intersection numbers for \(\mathbb{Z}\)-extensions of chaotic dynamical systems, including the \(\mathbb{Z}\)-periodic Lorentz gas and the geodesic flow on a \(\mathbb{Z}\)-cover of a negatively curved compact surface. We establish a functional limit theorem.On length spectrum rigidity of dispersing billiard systemshttps://zbmath.org/1544.370182024-11-01T15:51:55.949586Z"Osterman, Otto Vaughn"https://zbmath.org/authors/?q=ai:osterman.otto-vaughnSummary: We consider the class of dispersing billiard systems in the plane formed by removing three convex analytic scatterers satisfying the non-eclipse condition. The collision map in this system is conjugated to a subshift, providing a natural labeling of periodic points. We study the problem of marked length spectrum rigidity for this class of systems. We show that two such systems have the same marked length spectrum if and only if their collision maps are analytically conjugate to each other near a homoclinic orbit and that two scatterers and the marked length spectrum together uniquely determine the third scatterer. To do so, we conjugate the system to a Birkhoff normal form and show that the length spectral data of a certain class of periodic orbits can be expressed as a type of asymptotic power series expansion. We relate this asymptotic series to the power series of two analytic functions describing the dynamics of the normalized system and show that we can recover the full power series expansions of these functions.Tangent ray foliations and their associated outer billiardshttps://zbmath.org/1544.370192024-11-01T15:51:55.949586Z"Godoy, Yamile"https://zbmath.org/authors/?q=ai:godoy.yamile"Harrison, Michael"https://zbmath.org/authors/?q=ai:harrison.michael|harrison.michael-a|harrison.michael-c|harrison.michael-j|harrison.michael-douglas|harrison.michael-corin"Salvai, Marcos"https://zbmath.org/authors/?q=ai:salvai.marcosThe authors begin the paper with the simple fact that given a unit tangent vector field on the unit circle \({S}^1 \subset \mathbb{R}^2\), the corresponding tangent rays foliate the exterior of \({S}^1\).
In order to generalize this fact, it is a natural road to increase the dimensions and to change the curvature properties of the involved manifolds. Clearly, in even dimension \(2k\) the analogous problem for spheres \({S}^{2k-1} \subset \mathbb{R}^{2k}\) makes sense, however for \(\mathbb{R}^3\) it does not.
Outer billiars, originally popularized by \textit{J. Moser} [Stable and random motions in dynamical systems, Princeton, N. J., Princeton University Press (1973; Zbl 0271.70009)], provide a dynamical motivation. For each point \(x\) outside of a convex curve \(\gamma \subset \mathbb{R}^2\), there exists exactly one tangent ray to \(\gamma\) passing through \(x\), and the outer billiard map \(B\) is defined by reflecting \(x\) at the point of tangency. When attempting to define outer billiards in higher-dimensional Euclidean spaces, one encounters the following issue. Given a smooth closed strictly convex hypersurface \(N\), there are too many tangent lines passing through each point \(x\) outside of \(N\). By using the standard symplectic structure, \textit{S. Tabachnikov} [Adv. Math. 115, No. 2, 221--249 (1995; Zbl 0846.58038)] resolved this issue in the even-dimensional case.
With this in mind, one can fully understand authors' abstract: ``Let \(v\) be a unit vector field on a complete, umbilic (but not totally geodesic) hypersurface \(N\) in a space form; for example, on the unit sphere \(S^{2k-1} \subset \mathbb{R}^{2k}\) in even dimension, or on a horosphere in hyperbolic space. We give necessary and sufficient conditions on \(v\) for the rays with initial velocities \(v\) (and \(-v\)) to foliate the exterior \(U\) of \(N\). We find and explore relationships among these vector fields, geodesic vector fields, and contact structures on \(N\). When the rays corresponding to each of \(\pm v\) foliate \(U\), \(v\) induces an outer billiard map whose billiard table is \(U\). We describe the unit vector fields on \(N\) whose associated outer billiard map is volume preserving. Also we study a particular example in detail, namely, when \(N \simeq \mathbb{R}^3\) is a horosphere of the four-dimensional hyperbolic space and \(v\) is the unit vector field on \(N\) obtained by normalizing the stereographic projection of a Hopf vector field on \(S^3\). In the corresponding outer billiard map we find explicit periodic orbits, unbounded orbits, and bounded nonperiodic orbits. We conclude with several questions regarding the topology and geometry of bifoliating vector fields and the dynamics of their associated outer billiards.''
Reviewer: Jesus Muciño Raymundo (Morelia)Maximal transverse measures of expanding foliationshttps://zbmath.org/1544.370202024-11-01T15:51:55.949586Z"Ures, Raul"https://zbmath.org/authors/?q=ai:ures.raul"Viana, Marcelo"https://zbmath.org/authors/?q=ai:viana.marcelo"Yang, Fan"https://zbmath.org/authors/?q=ai:yang.fan.30"Yang, Jiagang"https://zbmath.org/authors/?q=ai:yang.jiagangSummary: For an expanding (unstable) foliation of a diffeomorphism, we use a natural dynamical averaging to construct transverse measures, which we call \textit{maximal}, describing the statistics of how the iterates of a given leaf intersect the cross-sections to the foliation. For a suitable class of diffeomorphisms, we prove that this averaging converges, even exponentially fast, and the limit measures have finite ergodic decompositions. These results are obtained through relating the maximal transverse measures to the maximal \(u\)-entropy measures of the diffeomorphism (see [\textit{R. Ures} et al., Ergodic Theory Dyn. Syst. 44, No. 1, 290--333 (2024; Zbl 1539.37042)]).Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifoldshttps://zbmath.org/1544.370212024-11-01T15:51:55.949586Z"Fenley, Sergio R."https://zbmath.org/authors/?q=ai:fenley.sergio-r"Potrie, Rafael"https://zbmath.org/authors/?q=ai:potrie.rafaelThis work investigates ergodicity of conservative \(C^{1+ \varepsilon}\) partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds via accessibility. It does so without recurring to perturbations arguments, while granting mixing as well.
The main result is that if \(f \in C^1\), where \(f\) is a partially hyperbolic diffeomorphism of a closed hyperbolic \(3\)-manifold such that the nonwandering set is the entire manifold, then \(f\) is accessible. Given such a result, by exploiting [\textit{K. Burns} and \textit{A. Wilkinson}, Ann. Math. (2) 171, No. 1, 451--489 (2010; Zbl 1196.37057)], the claimed statement on conservative systems can be recovered. The main result is proven by contradiction exploiting the geometry of foliations, based on previous results of \textit{F. Rodriguez Hertz} et al. [J. Mod. Dyn. 2, No. 2, 187--208 (2008; Zbl 1148.37019)].
The starting point is the fact that hyperbolic \(3\)-dimensional manifolds that can be obtained as a quotient of \(\mathbb{H}^3\) are abundant (thanks to the geometrization theorem). Based on the case analysis by \textit{F. Rodriguez Hertz} et al. [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 33, No. 4, 1023--1032 (2016; Zbl 1380.37067)], the authors prove that the obstruction to being accessible must be an invariant lamination whose leaves are saturated by stable and unstable manifolds, but this is not compatible with an hyperbolic manifold. Most of the analysis is carried in the setting of homeomorphisms homotopic to the identity (thus being flexible enough to be used beyond the main objective of study). In particular, the original dynamics can be lifted to a dynamic \(\tilde{f}\) which commutes with all deck transformations. Next, either \(\tilde{f}\) fixes at least a leaf of the (lifted) lamination or none is fixed. Both cases, which have to be taken care of with different tools, will lead to a contradiction with respect to the hyperbolicity of the manifold. Note that handling the second case leads the authors to obtain results on quasigeodesic pseudo-Anosov flows.
The article is well written: for the readers' sake longer proofs are first sketched and then broken down into readable lemmas, which can be adapted to several situations.
Reviewer: Paolo Giulietti (Pisa)Center foliation rigidity for partially hyperbolic toral diffeomorphismshttps://zbmath.org/1544.370222024-11-01T15:51:55.949586Z"Gogolev, Andrey"https://zbmath.org/authors/?q=ai:gogolev.andrey"Kalinin, Boris"https://zbmath.org/authors/?q=ai:kalinin.boris"Sadovskaya, Victoria"https://zbmath.org/authors/?q=ai:sadovskaya.victoriaThis article deals with rigidity results for perturbations of toral partially hyperbolic linear automorphisms.
More precisely, consider a partially hyperbolic automorphism \(L\) of the torus \(\mathbb T^d\), which is diagonalizable over \(\mathbb C\) and has a dense center foliation (in particular, this implies \(d\ge 3\)). Consider a \(C^\infty\) diffeomorphism \(f\) which is a small \(C^1\) perturbation \(f\) of \(L\). The question is: under which conditions is the diffeomorphism \(f\) smoothly conjugate to \(L\)?
This work deals with this question in three main cases.
\begin{itemize}
\item If the center foliation of \(f\) is \(C^\infty\), then \(f\) is \(C^\infty\) leaf-conjugate to \(L\);
\item If \(L\) is irreducible (i.e., it has no rational invariant subspaces) and ergodic, then there exists \(r=r(L)>0\) such that if the center foliation of \(f\) is \(C^r\) and \(f\) is conjugate to \(L\) by a bi-Hölder homeomorphism \(h\), then \(h\) is \(C^\infty\);
\item If \(L\) is irreducible and ergodic, and in the case of a 2-dimensional center, then the topological conjugacy is equivalent to the smooth conjugacy (and, also, the absence of accessibility).
\end{itemize}
A particularly interesting consequence of the second result is the case where \(f\) is symplectic, which allows to get rid of the hypothesis of smoothness of the center foliation. In other words, if \(L\) is irreducible and ergodic, and if \(f\) is a smooth symplectic diffeomorphism conjugate to \(L\) by a bi-Hölder homeomorphism \(h\), then \(h\) is \(C^\infty\).
Reviewer: Pierre-Antoine Guihéneuf (Paris)Invariant distributions and the transport twistor space of closed surfaceshttps://zbmath.org/1544.370232024-11-01T15:51:55.949586Z"Bohr, Jan"https://zbmath.org/authors/?q=ai:bohr.jan"Lefeuvre, Thibault"https://zbmath.org/authors/?q=ai:lefeuvre.thibault"Paternain, Gabriel P."https://zbmath.org/authors/?q=ai:paternain.gabriel-pSummary: We study transport equations on the unit tangent bundle of a closed oriented Riemannian surface and their links to the \textit{transport twistor space} of the surface (a complex surface naturally tailored to the geodesic vector field). We show that fibrewise holomorphic distributions invariant under the geodesic flow -- which play an important role in tensor tomography on surfaces -- form a \textit{unital algebra}, that is, multiplication of such distributions is well defined and continuous. We also exhibit a natural bijective correspondence between fibrewise holomorphic invariant distributions and genuine holomorphic functions on twistor space with polynomial blowup on the boundary of the twistor space. Additionally, when the surface is Anosov, we classify holomorphic line bundles over twistor space which are smooth up to the boundary. As a byproduct of our analysis, we obtain a quantitative version of a result of \textit{L. Flaminio} [C. R. Acad. Sci., Paris, Sér. I 315, No. 6, 735--738 (1992; Zbl 0772.58046)]
asserting that invariant distributions of the geodesic flow of a positively curved metric on \(\mathbb{S}^2\) are determined by their zeroth and first Fourier modes.
{\copyright} 2024 The Authors. \textit{Journal of the London Mathematical Society} is copyright {\copyright} London Mathematical Society.Correction to: ``Anosov flows, growth rates on covers and group extensions of subshifts''https://zbmath.org/1544.370242024-11-01T15:51:55.949586Z"Dougall, Rhiannon"https://zbmath.org/authors/?q=ai:dougall.rhiannon"Sharp, Richard"https://zbmath.org/authors/?q=ai:sharp.richard-wSummary: This note corrects an error in our paper [ibid. 223, No. 2, 445--483 (2021; Zbl 1467.37037)]. This leaves our main results, Theorem 1.1, Corollary 1.2, Theorem 1.3 and Theorem 5.1, unchanged. We also fill a gap in the arguments presented in Sect. 9; this requires a small modification to the results in this section.Holography of geodesic flows, harmonizing metrics, and billiards' dynamicshttps://zbmath.org/1544.370252024-11-01T15:51:55.949586Z"Katz, Gabriel"https://zbmath.org/authors/?q=ai:katz.gabrielIn earlier work the author [Inverse Probl. Imaging 13, No. 3, 597--633 (2019; Zbl 1415.37043)] described a more topological approach to some inverse scattering problems. In the present work these ideas are continued to study the geometry of scattering maps and of the dynamics of billiard maps. After some preparations involving traversing flows on manifolds with boundary, the geodesic flow on Riemannian manifolds is studied under some technical conditions. Several holography theorems relating properties of the associated scattering and billiard maps are developed. The main tool developed is a Lyapunov function defined on the spherical tangent space of the manifold together with a distinguished Riemannian metric with respect to which this function is harmonic.
Reviewer: Thomas B. Ward (Durham)Attractor-repeller collision and the heterodimensional dynamicshttps://zbmath.org/1544.370262024-11-01T15:51:55.949586Z"Chigarev, Vladimir"https://zbmath.org/authors/?q=ai:chigarev.vladimir"Kazakov, Alexey"https://zbmath.org/authors/?q=ai:kazakov.alexey-o"Pikovsky, Arkady"https://zbmath.org/authors/?q=ai:pikovsky.arkady-s(no abstract)Bifurcations and chaos in three-coupled ramp-type neuronshttps://zbmath.org/1544.370272024-11-01T15:51:55.949586Z"Horikawa, Yo"https://zbmath.org/authors/?q=ai:horikawa.yo(no abstract)Homoclinic chaos in a four-dimensional manifold piecewise linear systemhttps://zbmath.org/1544.370282024-11-01T15:51:55.949586Z"Huang, Qiu"https://zbmath.org/authors/?q=ai:huang.qiu"Liu, Yongjian"https://zbmath.org/authors/?q=ai:liu.yongjian"Li, Chunbiao"https://zbmath.org/authors/?q=ai:li.chunbiao"Liu, Aimin"https://zbmath.org/authors/?q=ai:liu.aimin(no abstract)Complicated boundaries of the attraction basin in a class of three-dimensional polynomial systemshttps://zbmath.org/1544.370292024-11-01T15:51:55.949586Z"Huang, Weisheng"https://zbmath.org/authors/?q=ai:huang.weisheng"Zhang, Yuhong"https://zbmath.org/authors/?q=ai:zhang.yuhong"Yang, Xiao-Song"https://zbmath.org/authors/?q=ai:yang.xiaosong(no abstract)On hyperbolic attractors in a modified complex Shimizu-Morioka systemhttps://zbmath.org/1544.370302024-11-01T15:51:55.949586Z"Kruglov, Vyacheslav"https://zbmath.org/authors/?q=ai:kruglov.vyacheslav-pavlovich"Sataev, Igor"https://zbmath.org/authors/?q=ai:sataev.igor-rustamovich(no abstract)The graph structure of the generalized discrete Arnold's cat maphttps://zbmath.org/1544.370312024-11-01T15:51:55.949586Z"Li, Chengqing"https://zbmath.org/authors/?q=ai:li.chengqing"Tan, Kai"https://zbmath.org/authors/?q=ai:tan.kai"Feng, Bingbing"https://zbmath.org/authors/?q=ai:feng.bingbing"Lü, Jinhu"https://zbmath.org/authors/?q=ai:lu.jinhuEditorial remark: No review copy delivered.Predicting chaotic statistics with unstable invariant torihttps://zbmath.org/1544.370322024-11-01T15:51:55.949586Z"Parker, Jeremy P."https://zbmath.org/authors/?q=ai:parker.jeremy-p"Ashtari, Omid"https://zbmath.org/authors/?q=ai:ashtari.omid"Schneider, Tobias M."https://zbmath.org/authors/?q=ai:schneider.tobias-m(no abstract)Chaotic dynamics arising from sliding heteroclinic cycles in 3D Filippov systemshttps://zbmath.org/1544.370332024-11-01T15:51:55.949586Z"Yang, Qigui"https://zbmath.org/authors/?q=ai:yang.qigui"Huang, Yousu"https://zbmath.org/authors/?q=ai:huang.yousu(no abstract)A shifted logistic maphttps://zbmath.org/1544.370342024-11-01T15:51:55.949586Z"Buscarino, Arturo"https://zbmath.org/authors/?q=ai:buscarino.arturo"Fortuna, Luigi"https://zbmath.org/authors/?q=ai:fortuna.luigi(no abstract)Multistability analysis of a piecewise map via bifurcationshttps://zbmath.org/1544.370352024-11-01T15:51:55.949586Z"Cassal-Quiroga, B. B."https://zbmath.org/authors/?q=ai:cassal-quiroga.b-b"Gilardi-Velázquez, H. E."https://zbmath.org/authors/?q=ai:gilardi-velazquez.hector-eduardo"Campos-Cantón, E."https://zbmath.org/authors/?q=ai:campos-canton.eric(no abstract)Correlation sum and recurrence determinism of interval mapshttps://zbmath.org/1544.370362024-11-01T15:51:55.949586Z"Mihoková, Michaela"https://zbmath.org/authors/?q=ai:mihokova.michaela(no abstract)Topological expansive Lorenz maps with a hole at critical pointhttps://zbmath.org/1544.370372024-11-01T15:51:55.949586Z"Sun, Yun"https://zbmath.org/authors/?q=ai:sun.yun"Li, Bing"https://zbmath.org/authors/?q=ai:li.bing.4|li.bing|li.bing.1|li.bing.6|li.bing.3"Ding, Yiming"https://zbmath.org/authors/?q=ai:ding.yimingSummary: Let \(f\) be an expansive Lorenz map and \(c\) be the critical point. The survivor set is denoted as \(S_f (H):=\{x\in [0,1]: f^n (x)\notin H, \forall n\geq 0\}\), where \(H\) is an open subinterval. Here we study the hole \(H=(a,b)\) with \(a\leq c \leq b\) and \(a\neq b\). We observe that the case \(a=c\) is equivalent to the hole at 0, and the case \(b=c\) is equivalent to the hole at 1. Given any expansive Lorenz map \(f\) with a hole \(H=(a,b)\) and \(S_f (H)\nsubseteqq \{0,1\}\), we prove that there exists a Lorenz map \(g\) such that \(\tilde{S}_f (H)\setminus \Omega (g)\) is countable, where \(\Omega (g)\) is the Lorenz-shift of \(g\) and \(\tilde{S}_f (H)\) is the symbolic representation of \(S_f (H)\). Moreover, let \(a\) be fixed, we also give a complete characterization of the maximal plateau \(I(b)\) such that for all \(\epsilon \in I(b), S^+_f (a,\epsilon)=S^+_f (a,b)\), and \(I(b)\) may degenerate to a single point \(b\). As an application, when \(f\) has an ergodic acim and \(a\) is fixed, we obtain that the topological entropy function \(\lambda_f (a):b\mapsto h_{top}(f|S_f (a,b))\) is a devil staircase. At the special case that \(f\) being an intermediate \(\beta\)-transformation, using the Ledrappier-Young formula, the Hausdorff dimension function \(\eta_f (a):b\mapsto \dim_{\mathcal{H}}(S_f (a,b))\) is naturally a devil staircase when fixing \(a\). All the results can be naturally extended to the case that \(b\) is fixed. As a result, we extend the devil staircases in [\textit{C. Kalle} et al., Ergodic Theory Dyn. Syst. 40, No. 9, 2482--2514 (2020; Zbl 1448.11153); \textit{N. Langeveld} and \textit{T. Samuel}, Acta Math. Hung. 170, No. 1, 269--301 (2023; Zbl 1538.11143); \textit{M. Urbański}, Ergodic Theory Dyn. Syst. 6, 295--309 (1986; Zbl 0631.58019)]
to expansive Lorenz maps with a hole at critical point.Rigidity for piecewise smooth circle homeomorphisms and certain GIETshttps://zbmath.org/1544.370382024-11-01T15:51:55.949586Z"Berk, Przemysław"https://zbmath.org/authors/?q=ai:berk.przemyslaw"Trujillo, Frank"https://zbmath.org/authors/?q=ai:trujillo.frankSummary: In this article, we prove a rigidity property for a class of generalized interval exchange transformations (GIETs), which contains the class of piecewise smooth circle homeomorphisms. More precisely, we show that if two piecewise \(C^3\) GIETs \(f\) and \(g\) with zero mean non-linearity are topologically conjugated, boundary-equivalent, have the same typical combinatorial rotation number and their renormalizations approach in an appropriate way the set of affine interval exchange transformations, then, their respective renormalizations converge to each other exponentially and the conjugating map is of class \(C^1\). In addition, if \(f\) and \(g\) are GIETs with rotation-type combinatorial data (i.e., they naturally define a piecewise smooth circle homeomorphism), have the same typical combinatorial rotation number, and they are break-equivalent as piecewise smooth circle homeomorphisms, then they are \(C^1\)-conjugated as circle maps.
This work provides the first rigidity results for GIETs not smoothly conjugated to IETs, and generalizes a previous result of \textit{K. Cunha} and \textit{D. Smania} [Adv. Math. 250, 193--226 (2014; Zbl 1295.37013)], concerning an exceptional class of circle maps, in the setting of piecewise \(C^3\) circle homeomorphisms.The attractor structure of functional connectivity in coupled logistic mapshttps://zbmath.org/1544.370392024-11-01T15:51:55.949586Z"Voutsa, Venetia"https://zbmath.org/authors/?q=ai:voutsa.venetia"Papadopoulos, Michail"https://zbmath.org/authors/?q=ai:papadopoulos.michail"Papadopoulou Lesta, Vicky"https://zbmath.org/authors/?q=ai:papadopoulou-lesta.vicky"Hütt, Marc-Thorsten"https://zbmath.org/authors/?q=ai:hutt.marc-thorsten(no abstract)A dichotomy for the dimension of solenoidal attractors on high dimensional spacehttps://zbmath.org/1544.370402024-11-01T15:51:55.949586Z"Ren, Haojie"https://zbmath.org/authors/?q=ai:ren.haojieSummary: We study dynamical systems generated by skew products:
\[
T: [0,1) \times \mathbb{C} \to [0,1) \times \mathbb{C} \qquad T(x,y)=(bx \mod 1, \gamma y+\phi (x))
\]
where integer \(b \geq 2\), \(\gamma \in \mathbb{C}\) are such that \(0<|\gamma|<1\), and \(\phi\) is a real analytic \(\mathbb{Z}\)-periodic function. Let \(\Delta \in [0,1)\) be such that \(\gamma =|\gamma| e^{2\pi i \Delta}\). For the case \(\Delta \notin \mathbb{Q}\) we prove the following dichotomy for the solenoidal attractor \(K^{\phi}_{b, \gamma}\) for \(T\): Either \(K^{\phi}_{b, \gamma}\) is the graph of a real analytic function, or the Hausdorff dimension of \(K^{\phi}_{b, \gamma}\) is equal to \(\min \{3, 1+\frac{\log b}{\log 1/|\gamma|}\}\). Furthermore, given \(b\) and \(\phi\), the former alternative only happens for countably many \(\gamma\) unless \(\phi\) is constant.Higher order terms of Mather's \(\beta\)-function for symplectic and outer billiardshttps://zbmath.org/1544.370412024-11-01T15:51:55.949586Z"Baracco, Luca"https://zbmath.org/authors/?q=ai:baracco.luca"Bernardi, Olga"https://zbmath.org/authors/?q=ai:bernardi.olga"Nardi, Alessandra"https://zbmath.org/authors/?q=ai:nardi.alessandraSummary: We compute explicitly the formal Taylor expansion of Mather's \(\beta\)-function up to seventh order terms for symplectic and outer billiards in a strictly-convex planar domain \(C\). In particular, we specify the third terms of the asymptotic expansions of the distance (in the sense of the symmetric difference metric) between \(C\) and its best approximating inscribed or circumscribed polygons with at most \(n\) vertices. We use tools from affine differential geometry.The hidden sensitivity of non-smooth dynamicshttps://zbmath.org/1544.370422024-11-01T15:51:55.949586Z"Catsis, Salvador"https://zbmath.org/authors/?q=ai:catsis.salvador"Hall, Cameron L."https://zbmath.org/authors/?q=ai:hall.cameron-luke"Jeffrey, Mike R."https://zbmath.org/authors/?q=ai:jeffrey.mike-rSummary: Switches in dynamical systems are known to exhibit wildly different behaviours depending on how they are modelled, for instance whether they occur as smooth transitions or abrupt jumps, and whether they involve delays or discrete perturbations. These differences arise because switches are sensitive to perturbation, but there is limited knowledge about where this sensitivity comes from. Here we take a switch in a simple one-dimensional system, then discretise time and introduce a small delay. The resulting system is described by a piecewise-linear map with incredibly complex dynamics, and is sensitive to parameter changes even if the time-steps and delays are made infinitesimally small. We show that this sensitivity reveals itself in the more versatile numerical tool of the \textit{transition count}, which captures the likelihood of switching occurring at any instant in a simulation. We use this to show that sensitivity to parameters persists in a system with two switches, where it then has large-scale dynamical effects. The use of transition counts in this way may prove a versatile tool for studying more complex switching processes in general.Hysteresis and universal bifurcation in natural processeshttps://zbmath.org/1544.370432024-11-01T15:51:55.949586Z"Tanyi, G. E."https://zbmath.org/authors/?q=ai:tanyi.g-eSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].Weak centers and local bifurcation of critical periods in a \(Z_2\)-equivariant vector field of degree 5https://zbmath.org/1544.370442024-11-01T15:51:55.949586Z"Wu, Yusen"https://zbmath.org/authors/?q=ai:wu.yusen"Li, Feng"https://zbmath.org/authors/?q=ai:li.feng(no abstract)Transition to anomalous dynamics in a simple random maphttps://zbmath.org/1544.370452024-11-01T15:51:55.949586Z"Yan, Jin"https://zbmath.org/authors/?q=ai:yan.jin"Majumdar, Moitrish"https://zbmath.org/authors/?q=ai:majumdar.moitrish"Ruffo, Stefano"https://zbmath.org/authors/?q=ai:ruffo.stefano"Sato, Yuzuru"https://zbmath.org/authors/?q=ai:sato.yuzuru"Beck, Christian"https://zbmath.org/authors/?q=ai:beck.christian"Klages, Rainer"https://zbmath.org/authors/?q=ai:klages.rainer(no abstract)Bifurcation of limit cycles by perturbing piecewise linear Hamiltonian systems with piecewise polynomialshttps://zbmath.org/1544.370462024-11-01T15:51:55.949586Z"Chen, Jiangbin"https://zbmath.org/authors/?q=ai:chen.jiangbin"Han, Maoan"https://zbmath.org/authors/?q=ai:han.maoan(no abstract)Phase space reaction dynamics associated with an index-2 saddle point for time-dependent Hamiltonian systemshttps://zbmath.org/1544.370472024-11-01T15:51:55.949586Z"Cao, Hengchang"https://zbmath.org/authors/?q=ai:cao.hengchang"Wiggins, Stephen"https://zbmath.org/authors/?q=ai:wiggins.stephen-r(no abstract)The Darboux polynomials and integrability of polynomial Levinson-Smith differential equationshttps://zbmath.org/1544.370482024-11-01T15:51:55.949586Z"Demina, Maria V."https://zbmath.org/authors/?q=ai:demina.maria-v(no abstract)Baxter operators in Ruijsenaars hyperbolic system. IV: Coupling constant reflection symmetry.https://zbmath.org/1544.370492024-11-01T15:51:55.949586Z"Belousov, Nikita"https://zbmath.org/authors/?q=ai:belousov.nikita"Derkachov, Sergey"https://zbmath.org/authors/?q=ai:derkachev.sergei-eduardovich"Kharchev, Sergey"https://zbmath.org/authors/?q=ai:kharchev.sergey"Khoroshkin, Sergey"https://zbmath.org/authors/?q=ai:khoroshkin.sergey-mIn this work, the authors present and investigate a new family of commuting Baxter operators for the Ruijsenaars hyperbolic system. By using a degeneration of Rains integral identity, they verify the commutativity between the two families of Baxter operators and leverage this to study the coupling constant symmetry of the wave function. Additionally, a connection between the new Baxter operators and the Noumi-Sano difference operators is established. This is the fourth in a series of papers by the authors dedicated to Baxter operators for the Ruijsenaars hyperbolic system.
Reviewer: Danilo Latini (Roma)Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation lawshttps://zbmath.org/1544.370502024-11-01T15:51:55.949586Z"Lou, S. Y."https://zbmath.org/authors/?q=ai:lou.senyue"Hao, Xia-zhi"https://zbmath.org/authors/?q=ai:hao.xiazhi"Jia, Man"https://zbmath.org/authors/?q=ai:jia.man.1Summary: Utilizing some conservation laws of \((1+1)\)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm. The algorithm can be applied to Lax pairs and higher order flows. In other words, if the original lower dimensional model is Lax integrable (possesses Lax pairs) and symmetry integrable (possesses infinitely many higher order symmetries and/or infinitely many conservation laws), then the deformed higher order systems are also Lax integrable and symmetry integrable. For concreteness, the deformation algorithm is applied to the usual \((1+1)\)-dimensional Korteweg-de Vries (KdV) equation and the \((1+1)\)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) system (including nonlinear Schrödinger (NLS) equation as a special example). It is interesting that the deformed \((3+1)\)-dimensional KdV equation is also an extension of the \((1+1)\)-dimensional Harry-Dym (HD) type equations which are reciprocal links of the \((1+1)\)-dimensional KdV equation. The Lax pairs of the \((3 + 1)\)-dimensional KdV-HD system and the \((2 + 1)\)-dimensional AKNS system are explicitly given. The higher order symmetries, i.e., the whole \((3 + 1)\)-dimensional KdV-HD hierarchy, are also explicitly obtained via the deformation algorithm. The single soliton solution of the \((3 + 1)\)-dimensional KdV-HD equation is implicitly given. Because of the effects of the deformation, the symmetric soliton shape of the usual KdV equation is no longer conserved and deformed to be asymmetric and/or multi-valued. The deformation conjecture holds for all the known \((1+1)\)-dimensional integrable local evolution systems that have been checked, and we have not yet found any counter-example so far. The introduction of a large number of \((D + 1)\)-dimensional integrable systems of this paper explores a serious challenge to all mathematicians and theoretical physicists because the traditional methods are no longer directly valid to solve these integrable equations.A combined Liouville integrable hierarchy associated with a fourth-order matrix spectral problemhttps://zbmath.org/1544.370512024-11-01T15:51:55.949586Z"Ma, Wen-Xiu"https://zbmath.org/authors/?q=ai:ma.wen-xiu|ma.wenxiu(no abstract)Linearization -- a unified approachhttps://zbmath.org/1544.370522024-11-01T15:51:55.949586Z"Anderson, R. L."https://zbmath.org/authors/?q=ai:anderson.rodney-l|anderson.richard-l|anderson.robert-lee|anderson.r-lucile|anderson.robert-leonard"Taflin, E."https://zbmath.org/authors/?q=ai:taflin.erikSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].On the Poisson structure and action-angle variables for the complex modified Korteweg-de Vries equationhttps://zbmath.org/1544.370532024-11-01T15:51:55.949586Z"Yin, Zhe-Yong"https://zbmath.org/authors/?q=ai:yin.zhe-yong"Tian, Shou-Fu"https://zbmath.org/authors/?q=ai:tian.shoufuSummary: In this paper, we employ the inverse scattering approach to study the Poisson structure and action-angle variables of the complex modified Korteweg-de Vries (cmKdV) equation. We first derive the cmKdV equation via the principle of variation. Then, we successfully obtain the Poisson brackets for the scattering data of the equation. Furthermore, the action-angle variables are expressed in terms of the scattering data. Interestingly, our results show that the coordinate expression and the spectral parameter expression of the Hamiltonian can be related by the conservation laws.The Sasa-Satsuma equation with high-order discrete spectra in space-time solitonic regions: soliton resolution via the mixed \(\bar{\partial}\)-Riemann-Hilbert problemhttps://zbmath.org/1544.370542024-11-01T15:51:55.949586Z"Zhang, Minghe"https://zbmath.org/authors/?q=ai:zhang.minghe"Yan, Zhenya"https://zbmath.org/authors/?q=ai:yan.zhenya(no abstract)On a new proof of the Okuyama-Sakai conjecturehttps://zbmath.org/1544.370552024-11-01T15:51:55.949586Z"Yang, Di"https://zbmath.org/authors/?q=ai:yang.di"Zhang, Qingsheng"https://zbmath.org/authors/?q=ai:zhang.qingshengSummary: \textit{K. Okuyama} and \textit{K. Sakai} [J. High Energy Phys. 2020, No. 10, Paper No. 160, 36 p. (2020; Zbl 1456.83116)]
gave a conjectural equality for the higher genus generalized Brézin-Gross-Witten (BGW) free energies. In a recent work [the authors, ``On the Hodge-BGW correspondence'', Preprint, \url{arXiv:2112.12736}], we established the Hodge-BGW correspondence on the relationship between certain special cubic Hodge integrals and the generalized BGW correlators, and a proof of the Okuyama-Sakai conjecture was also given \textit{ibid}. In this paper, we give a new proof of the Okuyama-Sakai conjecture by a further application of the Dubrovin-Zhang theory for the KdV hierarchy.Geometric realization of the Sasa-Satsuma equation on the symmetric space \(\mathrm{SU}(3)/\mathrm{U}(2)\)https://zbmath.org/1544.370562024-11-01T15:51:55.949586Z"Zhong, Shiping"https://zbmath.org/authors/?q=ai:zhong.shiping"Zhao, Zehui"https://zbmath.org/authors/?q=ai:zhao.zehuiSummary: The analytic property of the Sasa-Satsuma equation has been well-explored via using an array of mathematical tools (such as the inverse scattering transformation, the Hirota bilinear method and the Darboux transformation). This paper devotes to exploring geometric properties of this equation via the zero curvature representation in terms of the language in Yang-Mills theory. The generalized Landau-Lifshitz type model of Sym-Pohlmeyer moving curves evolving in the symmetric Lie algebra \(\mathbf{g} = \mathbf{k} \oplus \mathbf{m}\) with initial data being suitably restricted is gauge equivalent to the Sasa-Satsuma equation. This gives a geometric realization of the Sasa-Satsuma equation.The Virasoro-like algebra of a Frobenius manifoldhttps://zbmath.org/1544.370572024-11-01T15:51:55.949586Z"Liu, Si-Qi"https://zbmath.org/authors/?q=ai:liu.siqi"Yang, Di"https://zbmath.org/authors/?q=ai:yang.di"Zhang, Youjin"https://zbmath.org/authors/?q=ai:zhang.youjin"Zhou, Jian"https://zbmath.org/authors/?q=ai:zhou.jianThe authors propose the construction of an infinite-dimensional Lie algebra of Virasoro type that arises as a deformation of the usual Virasoro algebra of a Frobenius manifold. It is shown that this deformation contains besides the Virasoro algebra two other subalgebras of interest in physical applications. By means of the construction, a hierarchy of quadratic PDEs that are fulfilled by the genus-zero free energy of the Frobenius manifold is constructed. Extending some results from [\textit{B. Dubrovin} and \textit{Y. Zhang}, Sel. Math., New Ser. 5, No. 4, 423--466 (1999; Zbl 0963.81066)], and assuming that the calibrated Frobenius manifold is semisimple, the authors derive the Virasoro constraints for the corresponding abstract Hodge partition function.
Reviewer: Rutwig Campoamor Stursberg (Madrid)Noetherian symmetries, Bäcklund transformation and conservation laws for a completely integrable three-dimensional systemhttps://zbmath.org/1544.370582024-11-01T15:51:55.949586Z"Roy Chowdhury, A."https://zbmath.org/authors/?q=ai:roychowdhury.a-p|roychowdhury.ayan|roy-chowdhury.asesh|roychowdhury.arup|roy-chowdhury.a-n|roy-chowdhury.amberSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].Long-time asymptotics of solution to the coupled Hirota system with \(4 \times 4\) Lax pairhttps://zbmath.org/1544.370592024-11-01T15:51:55.949586Z"Liu, Nan"https://zbmath.org/authors/?q=ai:liu.nanSummary: We study the Cauchy problem for the integrable coupled Hirota system with a \(4 \times 4\) Lax pair on the line with decaying initial data. By deriving a Riemann-Hilbert representation for the solution, we compute the precise leading-order terms for long-time asymptotics based on the nonlinear steepest descent arguments.Long time stability for the derivative nonlinear Schrödinger equationhttps://zbmath.org/1544.370602024-11-01T15:51:55.949586Z"Liu, Jianjun"https://zbmath.org/authors/?q=ai:liu.jianjun|liu.jianjun.1"Xiang, Duohui"https://zbmath.org/authors/?q=ai:xiang.duohuiSummary: In this paper, we consider the long time dynamics of the solutions of the derivative nonlinear Schrödinger equation on one dimensional torus without external parameters. By using rational normal form, we prove the long time stability for generic small initial data.Cauchy matrix approach for \(\mathrm{H}1^a\) equation in the torqued Adler-Bobenko-Suris lattice listhttps://zbmath.org/1544.370612024-11-01T15:51:55.949586Z"Wang, Jing"https://zbmath.org/authors/?q=ai:wang.jing.243"Zhao, Song-lin"https://zbmath.org/authors/?q=ai:zhao.songlin"Shen, Shoufeng"https://zbmath.org/authors/?q=ai:shen.shoufeng(no abstract)Efficient forecasting of chaotic systems with block-diagonal and binary reservoir computinghttps://zbmath.org/1544.370622024-11-01T15:51:55.949586Z"Ma, Haochun"https://zbmath.org/authors/?q=ai:ma.haochun"Prosperino, Davide"https://zbmath.org/authors/?q=ai:prosperino.davide"Haluszczynski, Alexander"https://zbmath.org/authors/?q=ai:haluszczynski.alexander"Räth, Christoph"https://zbmath.org/authors/?q=ai:rath.christoph(no abstract)Fourier phase index for extracting signatures of determinism and nonlinear features in time serieshttps://zbmath.org/1544.370632024-11-01T15:51:55.949586Z"Aguilar-Hernández, Alberto Isaac"https://zbmath.org/authors/?q=ai:aguilar-hernandez.alberto-isaac"Serrano-Solis, David Michel"https://zbmath.org/authors/?q=ai:serrano-solis.david-michel"Ríos-Herrera, Wady A."https://zbmath.org/authors/?q=ai:rios-herrera.wady-a"Zapata-Berruecos, José Fernando"https://zbmath.org/authors/?q=ai:zapata-berruecos.jose-fernando"Vilaclara, Gloria"https://zbmath.org/authors/?q=ai:vilaclara.gloria"Martínez-Mekler, Gustavo"https://zbmath.org/authors/?q=ai:martinez-mekler.gustavo"Müller, Markus F."https://zbmath.org/authors/?q=ai:muller.markus-f(no abstract)A novel approach to the characterization of stretching and folding in pursuit tracking with chaotic and intermittent behaviorshttps://zbmath.org/1544.370642024-11-01T15:51:55.949586Z"Babazadeh, Fatemeh"https://zbmath.org/authors/?q=ai:babazadeh.fatemeh"Ahmadi-Pajouh, Mohammad Ali"https://zbmath.org/authors/?q=ai:ahmadi-pajouh.mohammad-ali"Reza Hashemi Golpayegani, Seyed Mohammad"https://zbmath.org/authors/?q=ai:hashemi-golpayegani.seyed-mohammad-reza(no abstract)Revealing system dimension from single-variable time serieshttps://zbmath.org/1544.370652024-11-01T15:51:55.949586Z"Börner, Georg"https://zbmath.org/authors/?q=ai:borner.georg"Haehne, Hauke"https://zbmath.org/authors/?q=ai:haehne.hauke"Casadiego, Jose"https://zbmath.org/authors/?q=ai:casadiego.jose"Timme, Marc"https://zbmath.org/authors/?q=ai:timme.marc(no abstract)Data-informed reservoir computing for efficient time-series predictionhttps://zbmath.org/1544.370662024-11-01T15:51:55.949586Z"Köster, Felix"https://zbmath.org/authors/?q=ai:koster.felix"Patel, Dhruvit"https://zbmath.org/authors/?q=ai:patel.dhruvit"Wikner, Alexander"https://zbmath.org/authors/?q=ai:wikner.alexander"Jaurigue, Lina"https://zbmath.org/authors/?q=ai:jaurigue.lina"Lüdge, Kathy"https://zbmath.org/authors/?q=ai:ludge.kathy(no abstract)Multi-moment multiscale local sample entropy and its application to complex physiological time serieshttps://zbmath.org/1544.370672024-11-01T15:51:55.949586Z"Li, Sange"https://zbmath.org/authors/?q=ai:li.sange"Shang, Pengjian"https://zbmath.org/authors/?q=ai:shang.pengjianSummary: The Multiscale Entropy (MSE) is an effective measure to quantify the dynamical complexity of complex systems, which has many successful applications in physiological and physical fields. It uses different scales to mean-coarse-grain the original series, and then calculates the sample entropy for each coarse-grained series. Inspired by the MSE, we in this paper propose the Multi-Moment Multiscale Local Sample Entropy (MMMLSE), which considers both mean-coarse-grained and standard-deviation-coarse-grained characteristics of the original series for each scale, to quantify the dynamical complexity of complex systems. We use simulated data \((1/f\) noise, white noise and logistic map) to test the performance of our proposed method, with results showing that the MMMLSE can accurately and effectively characterize these complex systems. The ability to preserve nonlinear dynamics of the proposed method is also proved by surrogate data and nonlinearity test experiment. Furthermore, we apply the MMMLSE to analyze physiological signals, and the MMMLSE reveals that the ill individuals have lower dynamical complexity at larger scales than the healthy ones, and the elder individuals have lower dynamical complexity at larger scales than the younger ones, which are consistent with the reality.Ordinal Poincaré sections: reconstructing the first return map from an ordinal segmentation of time serieshttps://zbmath.org/1544.370682024-11-01T15:51:55.949586Z"Shahriari, Zahra"https://zbmath.org/authors/?q=ai:shahriari.zahra"Algar, Shannon D."https://zbmath.org/authors/?q=ai:algar.shannon-dee"Walker, David M."https://zbmath.org/authors/?q=ai:walker.david-m"Small, Michael"https://zbmath.org/authors/?q=ai:small.michael(no abstract)Dynamical and statistical properties of estimated high-dimensional ODE models: the case of the Lorenz '05 type II modelhttps://zbmath.org/1544.370692024-11-01T15:51:55.949586Z"Pavšek, Aljaž"https://zbmath.org/authors/?q=ai:pavsek.aljaz"Horvat, Martin"https://zbmath.org/authors/?q=ai:horvat.martin"Kocijan, Juš"https://zbmath.org/authors/?q=ai:kocijan.jus(no abstract)Statistical performance of local attractor dimension estimators in non-axiom a dynamical systemshttps://zbmath.org/1544.370702024-11-01T15:51:55.949586Z"Pons, Flavio"https://zbmath.org/authors/?q=ai:pons.flavio-maria-emanuele"Messori, Gabriele"https://zbmath.org/authors/?q=ai:messori.gabriele"Faranda, Davide"https://zbmath.org/authors/?q=ai:faranda.davide(no abstract)A Monte Carlo approach to understanding the impacts of initial-condition uncertainty, model uncertainty, and simulation variability on the predictability of chaotic systems: perspectives from the one-dimensional logistic maphttps://zbmath.org/1544.370712024-11-01T15:51:55.949586Z"Aksoy, Altug"https://zbmath.org/authors/?q=ai:aksoy.altug(no abstract)Forecasting the duration of three connected wings in a generalized Lorenz modelhttps://zbmath.org/1544.370722024-11-01T15:51:55.949586Z"Brugnago, E. L."https://zbmath.org/authors/?q=ai:brugnago.eduardo-l"Felicio, C. C."https://zbmath.org/authors/?q=ai:felicio.c-c"Beims, M. W."https://zbmath.org/authors/?q=ai:beims.marcus-w(no abstract)De Broglie-Bohm analysis of a nonlinear membrane: from quantum to classical chaoshttps://zbmath.org/1544.370732024-11-01T15:51:55.949586Z"Lima, Henrique Santos"https://zbmath.org/authors/?q=ai:lima.henrique-santos"Paixão, Matheus M. A."https://zbmath.org/authors/?q=ai:paixao.matheus-m-a"Tsallis, Constantino"https://zbmath.org/authors/?q=ai:tsallis.constantino(no abstract)Computing invariant densities of a class of piecewise increasing mappingshttps://zbmath.org/1544.370742024-11-01T15:51:55.949586Z"Wang, Zi"https://zbmath.org/authors/?q=ai:wang.zi"Ding, Jiu"https://zbmath.org/authors/?q=ai:ding.jiu"Rhee, Noah"https://zbmath.org/authors/?q=ai:rhee.noah-h(no abstract)Machine learning based prediction of phase ordering dynamicshttps://zbmath.org/1544.370752024-11-01T15:51:55.949586Z"Chauhan, Swati"https://zbmath.org/authors/?q=ai:chauhan.swati"Mandal, Swarnendu"https://zbmath.org/authors/?q=ai:mandal.swarnendu"Yadav, Vijay"https://zbmath.org/authors/?q=ai:yadav.vijay-kumar|vijay.yadav"Jaiswal, Prabhat K."https://zbmath.org/authors/?q=ai:jaiswal.prabhat-k"Priya, Madhu"https://zbmath.org/authors/?q=ai:priya.madhu"Shrimali, Manish Dev"https://zbmath.org/authors/?q=ai:shrimali.manish-dev(no abstract)Hamiltonian neural networks with automatic symmetry detectionhttps://zbmath.org/1544.370762024-11-01T15:51:55.949586Z"Dierkes, Eva"https://zbmath.org/authors/?q=ai:dierkes.eva"Offen, Christian"https://zbmath.org/authors/?q=ai:offen.christian"Ober-Blöbaum, Sina"https://zbmath.org/authors/?q=ai:ober-blobaum.sina"Flaßkamp, Kathrin"https://zbmath.org/authors/?q=ai:flasskamp.kathrin(no abstract)Global forecasts in reservoir computershttps://zbmath.org/1544.370772024-11-01T15:51:55.949586Z"Harding, S."https://zbmath.org/authors/?q=ai:harding.stephen-m|harding.s-a|harding.simon-p|harding.s-f|harding.steven-n|harding.sue|harding.stephen-t"Leishman, Q."https://zbmath.org/authors/?q=ai:leishman.q"Lunceford, W."https://zbmath.org/authors/?q=ai:lunceford.w"Passey, D. J."https://zbmath.org/authors/?q=ai:passey.d-j"Pool, T."https://zbmath.org/authors/?q=ai:pool.t"Webb, B."https://zbmath.org/authors/?q=ai:webb.benjamin-z(no abstract)Exploring nonlinear dynamics and network structures in Kuramoto systems using machine learning approacheshttps://zbmath.org/1544.370782024-11-01T15:51:55.949586Z"Song, Je Ung"https://zbmath.org/authors/?q=ai:song.je-ung"Choi, Kwangjong"https://zbmath.org/authors/?q=ai:choi.kwangjong"Oh, Soo Min"https://zbmath.org/authors/?q=ai:oh.soo-min"Kahng, B."https://zbmath.org/authors/?q=ai:kahng.byung-jay|kahng.byeong-hoon|kahng.byungnam|kahng.byungik(no abstract)Learning transfer operators by kernel density estimationhttps://zbmath.org/1544.370792024-11-01T15:51:55.949586Z"Surasinghe, Sudam"https://zbmath.org/authors/?q=ai:surasinghe.sudam"Fish, Jeremie"https://zbmath.org/authors/?q=ai:fish.jeremie"Bollt, Erik M."https://zbmath.org/authors/?q=ai:bollt.erik-m(no abstract)Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computinghttps://zbmath.org/1544.370802024-11-01T15:51:55.949586Z"Tsuchiyama, Kohei"https://zbmath.org/authors/?q=ai:tsuchiyama.kohei"Röhm, André"https://zbmath.org/authors/?q=ai:rohm.andre.1"Mihana, Takatomo"https://zbmath.org/authors/?q=ai:mihana.takatomo"Horisaki, Ryoichi"https://zbmath.org/authors/?q=ai:horisaki.ryoichi"Naruse, Makoto"https://zbmath.org/authors/?q=ai:naruse.makoto(no abstract)Stability of periodic orbits and bifurcation analysis of ship roll oscillations in regular sea waveshttps://zbmath.org/1544.370812024-11-01T15:51:55.949586Z"Kumar, Ranjan"https://zbmath.org/authors/?q=ai:kumar.ranjan"Mitra, Ranjan Kumar"https://zbmath.org/authors/?q=ai:mitra.ranjan-kumar(no abstract)Jerk dynamics in the minimal universal model of laserhttps://zbmath.org/1544.370822024-11-01T15:51:55.949586Z"Ginoux, Jean-Marc"https://zbmath.org/authors/?q=ai:ginoux.jean-marc"Meucci, Riccardo"https://zbmath.org/authors/?q=ai:meucci.riccardo"Euzzor, Stefano"https://zbmath.org/authors/?q=ai:euzzor.stefano"Pugliese, Eugenio"https://zbmath.org/authors/?q=ai:pugliese.eugenio"Sprott, Julien Clinton"https://zbmath.org/authors/?q=ai:sprott.julien-clinton(no abstract)Spin chaos dynamics in classical random dipolar interactionshttps://zbmath.org/1544.370832024-11-01T15:51:55.949586Z"Momeni, M."https://zbmath.org/authors/?q=ai:momeni.mojgan|momeni.maryam|momeni.mostafa|momeni.mohsen|momeni.minoo(no abstract)Stochastic model corrections for reduced Lotka-Volterra models exhibiting mutual, commensal, competitive, and predatory interactionshttps://zbmath.org/1544.370842024-11-01T15:51:55.949586Z"Bandy, R."https://zbmath.org/authors/?q=ai:bandy.r"Morrison, R."https://zbmath.org/authors/?q=ai:morrison.rob-d|morrison.ralph|morrison.robbie|morrison.rebecca-e|morrison.richard-a|morrison.ron|morrison.robert-g|morrison.robert-d|morrison.robert-l-jun|morrison.richard-j|morrison.ronald-w(no abstract)Genesis of noise-induced multimodal chaotic oscillations in enzyme kinetics: stochastic bifurcations and sensitivity analysishttps://zbmath.org/1544.370852024-11-01T15:51:55.949586Z"Bashkirtseva, Irina"https://zbmath.org/authors/?q=ai:bashkirtseva.irina-adolfovna(no abstract)Dynamics and bifurcations in Filippov type of competitive and symbiosis systemshttps://zbmath.org/1544.370862024-11-01T15:51:55.949586Z"Cao, Nanbin"https://zbmath.org/authors/?q=ai:cao.nanbin"Zhang, Yue"https://zbmath.org/authors/?q=ai:zhang.yue.4|zhang.yue.2|zhang.yue"Liu, Xia"https://zbmath.org/authors/?q=ai:liu.xia.1(no abstract)Effectivity of the vaccination strategy for a fractional-order discrete-time SIC epidemic modelhttps://zbmath.org/1544.370872024-11-01T15:51:55.949586Z"Coll, Carmen"https://zbmath.org/authors/?q=ai:coll.carmen"Ginestar, Damián"https://zbmath.org/authors/?q=ai:ginestar.damian"Herrero, Alicia"https://zbmath.org/authors/?q=ai:herrero.alicia"Sánchez, Elena"https://zbmath.org/authors/?q=ai:sanchez.elenaSummary: Indirect disease transmission is modeled via a fractional-order discrete time Susceptible-Infected-Contaminant (SIC) model vaccination as a control strategy. Two control actions are considered, giving rise to two different models: the vaccine efficacy model and the vaccination impact model. In the first model, the effectiveness of the vaccine is analyzed by introducing a new parameter, while in the second model, the impact of the vaccine is studied incorporating a new variable into the model. Both models are studied giving population thresholds to ensure the eradication of the disease. In addition, a sensitivity analysis of the Basic Reproduction Number has been carried out with respect to the effectiveness of the vaccine, the fractional order, the vaccinated population rate and the exposure rate. This analysis has been undertaken to study its effect on the dynamics of the models. Finally, the obtained results are illustrated and discussed with a simulation example related to the evolution of the disease in a pig farm.Oscillatory dynamics induced by time delays in the quorum sensing system of Pseudomonas aeruginosahttps://zbmath.org/1544.370882024-11-01T15:51:55.949586Z"Gao, Chunyan"https://zbmath.org/authors/?q=ai:gao.chunyan"Chen, Fangqi"https://zbmath.org/authors/?q=ai:chen.fangqi(no abstract)An improved method of global dynamics: analyzing the COVID-19 model with time delays and exposed infectionhttps://zbmath.org/1544.370892024-11-01T15:51:55.949586Z"Guo, Songbai"https://zbmath.org/authors/?q=ai:guo.songbai"Xue, Yuling"https://zbmath.org/authors/?q=ai:xue.yuling"Yuan, Rong"https://zbmath.org/authors/?q=ai:yuan.rong.1"Liu, Maoxing"https://zbmath.org/authors/?q=ai:liu.maoxing(no abstract)Canard, homoclinic loop, and relaxation oscillations in a Lotka-Volterra system with Allee effect in predator populationhttps://zbmath.org/1544.370902024-11-01T15:51:55.949586Z"Li, Jun"https://zbmath.org/authors/?q=ai:li.jun.18"Li, Shimin"https://zbmath.org/authors/?q=ai:li.shimin"Wang, Xiaoling"https://zbmath.org/authors/?q=ai:wang.xiaoling(no abstract)Directional synchrony among self-propelled particles under spatial influencehttps://zbmath.org/1544.370912024-11-01T15:51:55.949586Z"Pal, Suvam"https://zbmath.org/authors/?q=ai:pal.suvam"Sar, Gourab Kumar"https://zbmath.org/authors/?q=ai:sar.gourab-kumar"Ghosh, Dibakar"https://zbmath.org/authors/?q=ai:ghosh.dibakar"Pal, Arnab"https://zbmath.org/authors/?q=ai:pal.arnab(no abstract)Hidden dynamics, multistability and synchronization of a memristive Hindmarsh-Rose modelhttps://zbmath.org/1544.370922024-11-01T15:51:55.949586Z"Qiao, Shuai"https://zbmath.org/authors/?q=ai:qiao.shuai"Gao, Chenghua"https://zbmath.org/authors/?q=ai:gao.chenghua(no abstract)Noise-induced switching in dynamics of oscillating populations coupled by migrationhttps://zbmath.org/1544.370932024-11-01T15:51:55.949586Z"Ryashko, Lev"https://zbmath.org/authors/?q=ai:ryashko.lev-borisovich"Belyaev, Alexander"https://zbmath.org/authors/?q=ai:belyaev.aleksandr-v|belyaev.alexander-g"Bashkirtseva, Irina"https://zbmath.org/authors/?q=ai:bashkirtseva.irina-adolfovna(no abstract)Mathematical modeling and dynamical analysis for tumor cells and tumor propagating cells controlled by G9a inhibitorshttps://zbmath.org/1544.370942024-11-01T15:51:55.949586Z"Shen, Juan"https://zbmath.org/authors/?q=ai:shen.juan"Yao, Zhihao"https://zbmath.org/authors/?q=ai:yao.zhihao"Tan, Xuewen"https://zbmath.org/authors/?q=ai:tan.xuewen"Zou, Xiufen"https://zbmath.org/authors/?q=ai:zou.xiufen(no abstract)Global dynamic analysis of a discontinuous infectious disease system with two thresholdshttps://zbmath.org/1544.370952024-11-01T15:51:55.949586Z"Wang, Dongshu"https://zbmath.org/authors/?q=ai:wang.dongshu"Luo, Shifan"https://zbmath.org/authors/?q=ai:luo.shifan"Li, Wenxiu"https://zbmath.org/authors/?q=ai:li.wenxiu(no abstract)Modeling the dynamics of a ratio-dependent Leslie-Gower predator-prey system with strong Allee effecthttps://zbmath.org/1544.370962024-11-01T15:51:55.949586Z"Xu, Hainan"https://zbmath.org/authors/?q=ai:xu.hainan"He, Daihai"https://zbmath.org/authors/?q=ai:he.daihai(no abstract)Complex dynamics of predator-prey systems with Allee effecthttps://zbmath.org/1544.370972024-11-01T15:51:55.949586Z"Zeng, Yanni"https://zbmath.org/authors/?q=ai:zeng.yanni"Yu, Pei"https://zbmath.org/authors/?q=ai:yu.pei(no abstract)Arbitrarily large heteroclinic networks in fixed low-dimensional state spacehttps://zbmath.org/1544.370982024-11-01T15:51:55.949586Z"Castro, Sofia B. S. D."https://zbmath.org/authors/?q=ai:castro.sofia-b-s-d"Lohse, Alexander"https://zbmath.org/authors/?q=ai:lohse.alexander(no abstract)Application of an intelligent control on economics dynamic system: the attractive invariant ellipsoid approachhttps://zbmath.org/1544.370992024-11-01T15:51:55.949586Z"Juarez-del-Toro, R."https://zbmath.org/authors/?q=ai:juarez-del-toro.r"Castrejón-Lozano, J. G."https://zbmath.org/authors/?q=ai:castrejon-lozano.j-g"Gomez-Rosales, C. A."https://zbmath.org/authors/?q=ai:gomez-rosales.c-a"López-Chavarría, S."https://zbmath.org/authors/?q=ai:lopez-chavarria.sSummary: In this paper, we explore the application of attractive ellipsoid methodology [\textit{A. Poznyak} et al., Attractive ellipsoids in robust control. Cham: Birkhäuser/Springer (2014; Zbl 1314.93006)] on a new demand and supply model. The balance between the demand and supply is expressed by the Lin and Yang model [\textit{Y. C. Li} and \textit{H. Yang}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 1, Article ID 1750016, 11 p. (2017; Zbl 1358.34053)], described by differential equations, even if in the such a demand-supply model, other factors change and have significant effect on demand-supply dynamics. Analysis is compared with the situation when the prices of most products do not stay close to their equilibrium values and the Li and Yang demand and supply model is described by both ordinary differential equation and differential algebraic equation system. To achieve a specific economic goal, we will be able to design a management strategy based on minimum size of the invariant attractive ellipsoid, associated with the dynamic system, with a good performance in the rejection of external disturbances. We can consider a new transformed problem instead of the original problem with respect to solvability and related questions. Theoretical results are illustrated by an example.Periodicity analysis of the logistic map over ring \(\mathbb{Z}_{3^n}\)https://zbmath.org/1544.371002024-11-01T15:51:55.949586Z"Lu, Xiaoxiong"https://zbmath.org/authors/?q=ai:lu.xiaoxiong"Xie, Eric Yong"https://zbmath.org/authors/?q=ai:xie.eric-yong"Li, Chengqing"https://zbmath.org/authors/?q=ai:li.chengqing(no abstract)The spark of synchronization in heterogeneous networks of chaotic mapshttps://zbmath.org/1544.371012024-11-01T15:51:55.949586Z"Montalbán, Antonio"https://zbmath.org/authors/?q=ai:montalban.antonio"Corder, Rodrigo M."https://zbmath.org/authors/?q=ai:corder.rodrigo-m(no abstract)Border collision bifurcations and coexisting attractors in an economic bimodal maphttps://zbmath.org/1544.371022024-11-01T15:51:55.949586Z"Foroni, Ilaria"https://zbmath.org/authors/?q=ai:foroni.ilaria(no abstract)Dynamic analysis of a new financial system with diffusion effect and two delayshttps://zbmath.org/1544.371032024-11-01T15:51:55.949586Z"Wu, Huiming"https://zbmath.org/authors/?q=ai:wu.huiming"Jiang, Zhichao"https://zbmath.org/authors/?q=ai:jiang.zhichao"Wu, Xiaoxue"https://zbmath.org/authors/?q=ai:wu.xiaoxue(no abstract)Dynamics of fractional-order chaotic Rocard relaxation econometric systemhttps://zbmath.org/1544.371042024-11-01T15:51:55.949586Z"Yao, Zhao"https://zbmath.org/authors/?q=ai:yao.zhao"Sun, Kehui"https://zbmath.org/authors/?q=ai:sun.kehui"He, Shaobo"https://zbmath.org/authors/?q=ai:he.shaobo(no abstract)Gap for geometric canonical height functionshttps://zbmath.org/1544.371052024-11-01T15:51:55.949586Z"Zhang, Yugang"https://zbmath.org/authors/?q=ai:zhang.yugangSummary: We prove the existence of a gap around zero for canonical height functions associated with endomorphisms of projective spaces defined over complex function fields. We also prove that if the rational points of height zero are Zariski dense, then the endomorphism is birationally isotrivial. As a corollary, by a result of \textit{S. Cantat} and \textit{J. Xie} [``Birational conjugacies between endomorphisms on the projective plane'', Preprint, \url{arXiv:2006.00051}], we have a geometric Northcott property on projective plane in the same spirit of results of \textit{R. L. Benedetto} [Int. Math. Res. Not. 2005, No. 62, 3855--3866 (2005; Zbl 1114.14018)], \textit{M. Baker} [J. Reine Angew. Math. 626, 205--233 (2009; Zbl 1187.37133)] and \textit{L. DeMarco} [Algebra Number Theory 10, No. 5, 1031--1056 (2016; Zbl 1391.37076)] on the projective line.On a self-similar behavior of logarithmic sumshttps://zbmath.org/1544.390172024-11-01T15:51:55.949586Z"Fedotov, A. A."https://zbmath.org/authors/?q=ai:fedotov.alexei-a|fedotov.andrey-a"Lukashova, I. I."https://zbmath.org/authors/?q=ai:lukashova.i-iSummary: The sums \({S}_N\left(\omega ,\zeta \right)=\sum_{n-0}^{N-1}1\ln\left(1+{e}^{-2\pi i\left(\omega n+\frac{\omega }{2}+\zeta \right)}\right),\) where \(\omega\) and \(\zeta\) are parameters, are related to trigonometric products from the theory of quasi-periodic operators as well as to a special function kindred to the Malyuzhinets function from the diffraction theory, the hyperbolic Ruijsenaars \(G\)-function, which arose in connection with the theory of integrable systems, and the Faddeev quantum dilogarithm, which plays an important role in the knot theory, Teichmuller quantum theory and the complex Chern-Simons theory. Assuming that \(\omega \in (0, 1)\) and \(\zeta \in \mathbb{C}_- \), we describe the behavior of logarithmic sums for large \(N\) using renormalization formulas similar to those well-known in the theory of Gaussian exponential sums.Mountain-climbing constructions for piecewise monotone functionshttps://zbmath.org/1544.390202024-11-01T15:51:55.949586Z"Wright, Stephen E."https://zbmath.org/authors/?q=ai:wright.stephen-eLet \(\mathcal{M}\) denote the class of continuous piecewise monotone functions of the unit interval \([0,1]\) to itself where 0 and 1 are fixed points. For continuous piecewise monotone functions \(f \in \mathcal{F}\) and \(g \in \mathcal{G}\), where \(\mathcal{F}\) and \(\mathcal{G}\) are among ten subclasses of \(\mathcal{M}\), the author constructs functions \(h \in \mathcal{G}\) and \(k \in \mathcal{F}\) such that \(f \circ h = g \circ k\). These results extend previous non-constructive proofs of \textit{J. V. Whittaker} [Can. J. Math. 18, 873--882 (1966; Zbl 0144.18006)] and \textit{R. Sikorski} and \textit{K. Zarankiewicz} [Fundam. Math. 41, 339--344 (1955; Zbl 0064.05501)] since properties of the functions \(h\) and \(k\) are found. For instance, \(h\) and \(k\) are piecewise monotone and Lipschitz continuous. The motivation for this type of problem is the mountain-climbing problem, where \(f\) and \(g\) are profiles of paths of mountain climbers. The functions \(h\) and \(k\) coordinate the profiles so that the climbers are at the same altitude at the same time.
Reviewer: Steve Pederson (Atlanta)Group extensions preserve almost finitenesshttps://zbmath.org/1544.460552024-11-01T15:51:55.949586Z"Naryshkin, Petr"https://zbmath.org/authors/?q=ai:naryshkin.petrSummary: We show that a free action \(G \curvearrowright X\) is almost finite if its restriction to some infinite normal subgroup of \(G\) is almost finite. Consider the class of groups which contains all infinite groups of locally subexponential growth and is closed under taking direct limits and extensions on the right by any amenable group. It follows that all free actions of a group from this class on finite-dimensional spaces are almost finite and therefore that minimal such actions give rise to classifiable crossed products. In particular, that gives a much easier proof for the recent result of Kerr and the author [\textit{D.~Kerr} and \textit{P.~Naryshkin}, ``Elementary amenability and almost finiteness'', Preprint, \url{arXiv:2107.05273}] on elementary amenable groups.Geometric methods in physics XL, workshop, Białowieża, Poland, June 20--25, 2023https://zbmath.org/1544.530032024-11-01T15:51:55.949586ZPublisher's description: This volume collects papers based on lectures given at the XL Workshop on Geometric Methods in Physics, held in Białowieża, Poland in July 2023. These chapters provide readers an overview of cutting-edge research in infinite-dimensional groups, integrable systems, quantum groups, Lie algebras and their generalizations and a wide variety of other areas. Specific topics include:
\begin{itemize}
\item Yang-Baxter equation
\item The restricted Siegel disc and restricted Grassmannian
\item Geometric and deformation quantization
\item Degenerate integrability
\item Lie algebroids and groupoids
\item Skew braces
\end{itemize}
Geometric Methods in Physics XL will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.
The articles of this volume will be reviewed individually. For the preceding conference see [Zbl 1531.53004].
Indexed articles:
\textit{Dobrogowska, Alina; Goliński, Tomasz; Sliżewska, Aneta; Kielanowski, Piotr}, 40 years of the workshop with Anatol Odzijewicz, 1-8 [Zbl 07919694]
\textit{Wiley-Bohm, Darlene; Kielanowski, Piotr; Schleich, Wolfgang P.}, Wigner Medal 2023, 9-15 [Zbl 07919695]
\textit{Barletta, Elisabetta; Dragomir, Sorin; Esposito, Francesco}, On the geometry of coherent state maps, 19-40 [Zbl 07919697]
\textit{Beltiţă, Daniel; Larotonda, Gabriel}, Groupoid techniques in operator theory, 41-48 [Zbl 07919698]
\textit{Goliński, Tomasz; Tumpach, Alice Barbora}, Integrable system on partial isometries: a finite-dimensional picture, 49-57 [Zbl 07919699]
\textit{Gay-Balmaz, François; Ratiu, Tudor S.; Tumpach, Alice B.}, The restricted Siegel disc as coadjoint orbit, 59-79 [Zbl 07919700]
\textit{Kijowski, Jerzy}, Geometric quantization (55 years later), 81-102 [Zbl 07919701]
\textit{Takeuchi, Tsukasa; Yoshimi, Naoko; Yoshioka, Akira}, Deformation of functions by star product, 103-112 [Zbl 07919702]
\textit{Brzeziński, Tomasz}, Special normalised affine matrices: an example of a Lie affgebra, 115-125 [Zbl 07919704]
\textit{Lechner, Gandalf}, Twisted Araki-Woods algebras, the Yang-Baxter equation, and quantum field theory, 127-144 [Zbl 07919705]
\textit{Rybołowicz, Bernard}, Skew braces and the braid equation on sets, 145-152 [Zbl 07919706]
\textit{Vendramin, Leandro}, Skew braces: a brief survey, 153-175 [Zbl 07919707]
\textit{Acevedo, Alfonso S.; Breton, Nora}, How birefringence arises from nonlinear electrodynamics, 179-188 [Zbl 07919709]
\textit{Bardadyn, Krzysztof}, \(L^p\)-Cuntz algebras and spectrum of weighted composition operators, 189-198 [Zbl 07919710]
\textit{Barron, Tatyana; Francis, Michael}, On automorphisms of complex \(b^k\)-manifolds, 199-207 [Zbl 07919711]
\textit{Blaschke, Petr}, Spherical pedal coordinates and calculus of variations, 209-221 [Zbl 07919712]
\textit{Chavez, Johan M.}, Higher-order curvature corrections in the Raychaudhuri equation, 223-231 [Zbl 07919713]
\textit{Doikou, Anastasia}, Yangians as pre-Lie and tridendriform algebras, 233-250 [Zbl 07919714]
\textit{Doliwa, Adam}, Hermite-Padé approximation, multiple orthogonal polynomials, and multidimensional Toda equations, 251-274 [Zbl 07919715]
\textit{Ellingsen, Ask; Lundholm, Douglas; Magnot, Jean-Pierre}, ``The six blind men and the elephant'': an interdisciplinary selection of measurement features, 275-307 [Zbl 07919716]
\textit{Fehér, László}, Notes on the degenerate integrability of reduced systems obtained from the master systems of free motion on cotangent bundles of compact Lie groups, 309-330 [Zbl 07919717]
\textit{Goldstein, Piotr P.}, A quadric of kinetic energy in the role of phase diagrams -- application to the Belinski-Khalatnikov-Lifshitz scenario, 331-347 [Zbl 07919718]
\textit{Harnad, J.}, Hamiltonian structure of isomonodromic deformation dynamics in linear systems of PDE's, 349-366 [Zbl 07919719]
\textit{Hounkonnou, Mahouton Norbert}, Discrete mechanics in nonuniform time \(\alpha\)-lattices, 367-381 [Zbl 07919720]
\textit{Ikeda, Yasushi}, Quantum derivation and Mishchenko-Fomenko construction, 383-391 [Zbl 07919721]
\textit{Kanatchikov, Igor V.; Kholodnyi, Valery A.}, The Milgromian acceleration of MOND and the cosmological constant from precanonical quantum gravity, 393-401 [Zbl 07919722]
\textit{Khimshiashvili, Giorgi}, A note on three collinear point charges, 403-412 [Zbl 07919723]
\textit{Mielnik, Bogdan; Fuentes, Jesús}, Conceptual problems in quantum squeezing, 413-426 [Zbl 07919724]
\textit{Navrátil, Dušan}, Lie symmetry analysis of the Charney-Hasegawa-Mima equation, 427-435 [Zbl 07919725]
\textit{Pasikhani, Fatemeh Nikzad; Mohammadi, Mohammad; Varsaie, Saad}, Stability theorem for \(\mathbb{Z}_2^n\)-Lie supergroups, 437-440 [Zbl 07919726]
\textit{Prykarpatski, Anatolij K.; Bovdi, Victor A.}, The Courant type algebroids, the coadjoint orbits, and related integrable flows, 441-452 [Zbl 07919727]
\textit{Panasyuk, Andriy}, Kronecker webs and nonlinear PDEs, 455-471 [Zbl 07919729]Symplectic non-convexity of toric domainshttps://zbmath.org/1544.530792024-11-01T15:51:55.949586Z"Dardennes, Julien"https://zbmath.org/authors/?q=ai:dardennes.julien"Gutt, Jean"https://zbmath.org/authors/?q=ai:gutt.jean"Zhang, Jun"https://zbmath.org/authors/?q=ai:zhang.jun.8|zhang.jun.11|zhang.jun.42|zhang.jun.31|zhang.jun.36|zhang.jun.12|zhang.jun.34|zhang.jun.1|zhang.jun|zhang.jun.16|zhang.jun.59|zhang.jun.37|zhang.jun.9|zhang.jun.6|zhang.jun.43|zhang.jun.7|zhang.jun.27|zhang.jun.5|zhang.jun.15|zhang.jun.29|zhang.jun.23|zhang.jun.2|zhang.jun.26|zhang.jun.17|zhang.jun.10Authors' abstract: We investigate the convexity up to symplectomorphism (called symplectic convexity) of star-shaped toric domains in \(\mathbb{R}^4\). In particular, based on the criterion from \textit{J. Chaidez} and \textit{O. Edtmair} [Invent. Math. 229, No. 1, 243--301 (2022; Zbl 1506.37056)] via Ruelle invariant and systolic ratio of the boundary of star-shaped toric domains, we provide elementary operations on domains that can kill the symplectic convexity. These operations only result in small perturbations in terms of domain's volume. Moreover, one of the operations is a systematic way to produce examples of dynamically convex but not symplectically convex toric domains. Finally, we are able to provide concrete bounds for the constants that appear in Chaidez-Edtmair's criterion.
Reviewer: Alexander Felshtyn (Szczecin)Bordism classes of loops and Floer's equation in cotangent bundleshttps://zbmath.org/1544.530872024-11-01T15:51:55.949586Z"Broćić, Filip"https://zbmath.org/authors/?q=ai:brocic.filip"Cant, Dylan"https://zbmath.org/authors/?q=ai:cant.dylanSummary: For each representative \(\mathfrak{B}\) of a bordism class in the free loop space of a manifold, we associate a moduli space of finite length Floer cylinders in the cotangent bundle. The left end of the Floer cylinder is required to be a lift of one of the loops in \(\mathfrak{B}\), and the right end is required to lie on the zero section. Under certain assumptions on the Hamiltonian functions, the length of the Floer cylinder is a smooth proper function, and evaluating the level sets at the right end produces a family of loops cobordant to \(\mathfrak{B}\). The argument produces arbitrarily long Floer cylinders with certain properties. We apply this to prove an existence result for 1-periodic orbits of certain Hamiltonian systems in cotangent bundles, and also to estimate the relative Gromov width of starshaped domains in certain cotangent bundles. The moduli space is similar to moduli spaces considered in [\textit{M. Abouzaid}, J. Symplectic Geom. 10, No. 1, 27--79 (2012; Zbl 1298.53092); \textit{A. Abbondandolo} and \textit{A. Figalli}, J. Differ. Equations 234, No. 2, 626--653 (2007; Zbl 1114.37034)] and [\textit{A. Abbondandolo} and \textit{M. Schwarz}, Geom. Topol. 14, No. 3, 1569--1722 (2010; Zbl 1201.53087)] for Tonelli Hamiltonians. The Hamiltonians we consider are not Tonelli, but rather of ``contact-type'' in the symplectization end.Time-inhomogeneous diffusion geometry and topologyhttps://zbmath.org/1544.550062024-11-01T15:51:55.949586Z"Huguet, Guillaume"https://zbmath.org/authors/?q=ai:huguet.guillaume"Tong, Alexander"https://zbmath.org/authors/?q=ai:tong.alexander"Rieck, Bastian"https://zbmath.org/authors/?q=ai:rieck.bastian"Huang, Jessie"https://zbmath.org/authors/?q=ai:huang.jessie"Kuchroo, Manik"https://zbmath.org/authors/?q=ai:kuchroo.manik"Hirn, Matthew"https://zbmath.org/authors/?q=ai:hirn.matthew-j"Wolf, Guy"https://zbmath.org/authors/?q=ai:wolf.guy"Krishnaswamy, Smita"https://zbmath.org/authors/?q=ai:krishnaswamy.smitaSummary: Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of high-dimensional data. Diffusion condensation is constructed as a time-inhomogeneous process where each step first computes a diffusion operator and then applies it to the data. We theoretically analyze the convergence and evolution of this process from geometric, spectral, and topological perspectives. From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel. Our spectral results are of particular interest since most of the literature on data diffusion is focused on homogeneous processes. From a topological perspective, we show that diffusion condensation generalizes centroid-based hierarchical clustering. We use this perspective to obtain a bound based on the number of data points, independent of their location. To understand the evolution of the data geometry beyond convergence, we use topological data analysis. We show that the condensation process itself defines an intrinsic condensation homology. We use this intrinsic topology, as well as the ambient persistent homology, of the condensation process to study how the data changes over diffusion time. We demonstrate both types of topological information in well-understood toy examples. Our work gives theoretical insight into the convergence of diffusion condensation and shows that it provides a link between topological and geometric data analysis.The relevance of René Thom. The morphological dimension in today's scienceshttps://zbmath.org/1544.580022024-11-01T15:51:55.949586ZPublisher's description: The body of work presented in this book comes from research carried out since 2017 as part of the international ``Actualité de René Thom'' project. This project was initially entitled ``Morphology and qualitative dynamics: Knowledge of forms / Forms of knowledge''. Subsequently, the name ``Relevance of René Thom'' was chosen for its clarity and evocative power.
The aim of this research project is to promote the scientific relevance of René Thom's thinking on forms, and to demonstrate the importance of his method and discoveries. It is based on discussions of Thom's thinking and the method he proposes -- i.e., to seek out dynamic structures in order to understand changes of form in nature and at the human-social level, to explain the transformation of these dynamic forms, to study the morphologies of process in various fields in order to advance scientific knowledge...
The relevance of this thinker has manifested itself in the form of monthly sessions of a research seminar, held from 2017 to 2022, as well as in the form of international congresses (2018, 2019), bringing together the greatest friends and continuators, both of the work of René Thom himself, and of reflection on morphogenetic dynamics in the most diverse disciplines. This created a space for dialogue and listening between the exact sciences and the social and human sciences. Indeed, the fields of study are necessarily interdisciplinary, since, as René Thom teaches us, morphological organization, or form, in its exchanges with matter, must be considered as ``independent'' of its substrate, i.e. the environment in which this morphogenesis unfolds.
Finally, this book marks a symbolic moment: it takes shape in the year that marks the centenary of the birth of René Thom, who was born in the French town of Montbéliard in 1923. To mark this centenary (1923--2023), a number of initiatives have been launched to celebrate the discoveries and advances of this mathematician-philosopher, ashe liked to call himself \dots The publication of the present book is one more, which we hope will shed light that will stimulate the morphological gaze Thom so urged us to adopt.
The articles of this volume will be reviewed individually.Jet bundle technique, Lie Bäcklund vector fields and diffusion equationshttps://zbmath.org/1544.580182024-11-01T15:51:55.949586Z"Steeb, W.-H."https://zbmath.org/authors/?q=ai:steeb.willi-hans"Strampp, W."https://zbmath.org/authors/?q=ai:strampp.walterSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisationhttps://zbmath.org/1544.600662024-11-01T15:51:55.949586Z"Huang, Yuanfei"https://zbmath.org/authors/?q=ai:huang.yuanfei"Huang, Qiao"https://zbmath.org/authors/?q=ai:huang.qiao"Duan, Jinqiao"https://zbmath.org/authors/?q=ai:duan.jinqiaoSummary: The most probable transition paths (MPTPs) of a stochastic dynamical system are the global minimisers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange (EL) equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary characterisation for the MPTPs of stochastic dynamical systems with Brownian noise. We prove that, under appropriate conditions, the MPTPs are completely determined by a first-order ordinary differential equation. The equivalence is established by showing that the Onsager-Machlup action functional of the original system can be derived from the corresponding Markovian bridge process. For linear stochastic systems and the nonlinear Hongler's model, the first-order differential equations determining the MPTPs are shown analytically to imply the EL equations of the Onsager-Machlup functional. For general nonlinear systems, the determining first-order differential equations can be approximated, in a short time or for the small noise case. Some numerical experiments are presented to illustrate our results.
{{\copyright} 2023 IOP Publishing Ltd \& London Mathematical Society}Stochastic energy-balance model with a moving ice linehttps://zbmath.org/1544.600732024-11-01T15:51:55.949586Z"Pavlyukevich, Ilya"https://zbmath.org/authors/?q=ai:pavlyukevich.ilya"Ritsch, Marian"https://zbmath.org/authors/?q=ai:ritsch.marianSummary: In [SIAM J. Appl. Dyn. Syst. 12, No. 4, 2068--2092 (2013; Zbl 1290.37033)], \textit{E. R. Widiasih} proposed and analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model with a moving ice line. In this paper, we extend this model to the stochastic setting and analyze it within the framework of stochastic slow-fast systems. We derive the dynamics for the ice line in the limit of a small parameter as a solution to a stochastic differential equation. The stochastic approach enables the study of co-existing (metastable) climate states as well as the transition dynamics between them.On the existence and uniqueness of stationary distributions for some piecewise deterministic Markov processes with state-dependent jump intensityhttps://zbmath.org/1544.600782024-11-01T15:51:55.949586Z"Czapla, Dawid"https://zbmath.org/authors/?q=ai:czapla.dawidSummary: In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate, between which the trajectory is driven by one of the given semiflows. We prove that there is a one-to-one correspondence between stationary distributions of such processes and those of the Markov chains given by their post-jump locations. Using this result, we further establish a criterion guaranteeing the existence and uniqueness of the stationary distribution in a particular case, where the post-jump locations result from the action of a random iterated function system with an arbitrary set of transformations.Sign patterns symbolization and its use in improved dependence test for complex network inferencehttps://zbmath.org/1544.623012024-11-01T15:51:55.949586Z"Yamashita Rios de Sousa, Arthur Matsuo"https://zbmath.org/authors/?q=ai:yamashita-rios-de-sousa.arthur-matsuo"Hlinka, Jaroslav"https://zbmath.org/authors/?q=ai:hlinka.jaroslav(no abstract)Convergence and robustness of bounded recurrent neural networks for solving dynamic Lyapunov equationshttps://zbmath.org/1544.650642024-11-01T15:51:55.949586Z"Wang, Guancheng"https://zbmath.org/authors/?q=ai:wang.guancheng"Hao, Zhihao"https://zbmath.org/authors/?q=ai:hao.zhihao"Zhang, Bob"https://zbmath.org/authors/?q=ai:zhang.bob"Jin, Long"https://zbmath.org/authors/?q=ai:jin.longSummary: Recurrent neural networks have been reported as an effective approach to solve dynamic Lyapunov equations, which widely exist in various application fields. Considering that a bounded activation function should be imposed on recurrent neural networks to solve the dynamic Lyapunov equation in certain situations, a novel bounded recurrent neural network is defined in this paper. Following the definition, several bounded activation functions are proposed, and two of them are used to construct the bounded recurrent neural network for demonstration, where one activation function has a finite-time convergence property and the other achieves robustness against noise. Moreover, theoretical analyses provide rigorous and detailed proof of these superior properties. Finally, extensive simulation results, including comparative numerical simulations and two application examples, are demonstrated to verify the effectiveness and feasibility of the proposed bounded recurrent neural network.Revisiting Gilbert Strang's ``A chaotic search for \(i\)''https://zbmath.org/1544.650782024-11-01T15:51:55.949586Z"Li, Ao"https://zbmath.org/authors/?q=ai:li.ao"Corless, Robert M."https://zbmath.org/authors/?q=ai:corless.robert-mAn efficient numerical method for fractional model of allelopathic stimulatory phytoplankton species with Mittag-Leffler lawhttps://zbmath.org/1544.651922024-11-01T15:51:55.949586Z"Ghanbari, Behzad"https://zbmath.org/authors/?q=ai:ghanbari.behzad"Kumar, Devendra"https://zbmath.org/authors/?q=ai:kumar.devendra.3"Singh, Jagdev"https://zbmath.org/authors/?q=ai:singh.jagdevSummary: The principal aim of the present article is to study a mathematical pattern of interacting phytoplankton species. The considered model involves a fractional derivative which enjoys a nonlocal and nonsingular kernel. We first show that the problem has a solution, then the proof of the uniqueness is included by means of the fixed point theory. The numerical solution of the mathematical model is also obtained by employing an efficient numerical scheme. From numerical simulations, one can see that this is a very efficient method and provides precise and outstanding results.Right and left inverse scattering problems formulations for the Zakharov-Shabat systemhttps://zbmath.org/1544.652322024-11-01T15:51:55.949586Z"Chernyavsky, Alexander E."https://zbmath.org/authors/?q=ai:chernyavsky.alexander-e"Frumin, Leonid L."https://zbmath.org/authors/?q=ai:frumin.leonid-l"Gelash, Andrey A."https://zbmath.org/authors/?q=ai:gelash.andrey-aSummary: We consider right and left formulations of the inverse scattering problem for the Zakharov-Shabat system and the corresponding integral Gelfand-Levitan-Marchenko equations. Both formulations are helpful for numerical solving of the inverse scattering problem, which we perform using the previously developed Toeplitz Inner Bordering (TIB) algorithm. First, we establish general relations between the right and left scattering coefficients. Then we propose an auxiliary kernel of the left Gelfand-Levitan-Marchenko equations, which allows one to solve the right scattering problem numerically. We generalize the TIB algorithm, initially proposed in the left formulation, to the right scattering problem case with the obtained formulas. The test runs of the TIB algorithm illustrate our results reconstructing the various non-symmetrical potentials from their right scattering data.Visual analytics to identify temporal patterns and variability in simulations from cellular automatahttps://zbmath.org/1544.681002024-11-01T15:51:55.949586Z"Giabbanelli, Philippe J."https://zbmath.org/authors/?q=ai:giabbanelli.philippe-j"Baniukiewicz, Magda"https://zbmath.org/authors/?q=ai:baniukiewicz.magdaDecomposition and factorisation of transients in functional graphshttps://zbmath.org/1544.681112024-11-01T15:51:55.949586Z"Doré, François"https://zbmath.org/authors/?q=ai:dore.francois"Formenti, Enrico"https://zbmath.org/authors/?q=ai:formenti.enrico"Porreca, Antonio E."https://zbmath.org/authors/?q=ai:porreca.antonio-e"Riva, Sara"https://zbmath.org/authors/?q=ai:riva.saraSummary: Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be quite large, it is interesting to decompose and factorise them into several subgraphs acting together. Polynomial equations over functional graphs provide a formal way to represent this decomposition and factorisation mechanism, and solving them validates or invalidates hypotheses on their decomposability. The current solution method breaks down a single equation into a series of \textit{basic} equations of the form \(A \times X = B\) (with \(A\), \(X\), and \(B\) being FGs) to identify the possible solutions. However, it is able to consider just FGs made of cycles only. This work proposes an algorithm for solving these basic equations for general connected FGs. By exploiting a connection with the cancellation problem, we prove that the upper bound to the number of solutions is closely related to the size of the cycle in the coefficient \(A\) of the equation. The cancellation problem is also involved in the main algorithms provided by the paper. We introduce a polynomial-time semi-decision algorithm able to provide constraints that a potential solution will have to satisfy if it exists. Then, exploiting the ideas introduced in the first algorithm, we introduce a second exponential-time algorithm capable of finding all solutions by integrating several `hacks' that try to keep the exponential as tight as possible.Learning reactive islands of the Voter97 systemhttps://zbmath.org/1544.681182024-11-01T15:51:55.949586Z"Hind, Alexander"https://zbmath.org/authors/?q=ai:hind.alexander"Wiggins, Stephen"https://zbmath.org/authors/?q=ai:wiggins.stephen-r(no abstract)Bifurcations and transition to chaos in generalized fractional maps of the orders \(0 < \alpha < 1\)https://zbmath.org/1544.700202024-11-01T15:51:55.949586Z"Edelman, Mark"https://zbmath.org/authors/?q=ai:edelman.mark"Helman, Avigayil B."https://zbmath.org/authors/?q=ai:helman.avigayil-b"Smidtaite, Rasa"https://zbmath.org/authors/?q=ai:smidtaite.rasa(no abstract)Transition to period-3 synchronized state in coupled Gauss mapshttps://zbmath.org/1544.700212024-11-01T15:51:55.949586Z"Gaiki, Pratik M."https://zbmath.org/authors/?q=ai:gaiki.pratik-m"Deshmukh, Ankosh D."https://zbmath.org/authors/?q=ai:deshmukh.ankosh-d"Pakhare, Sumit S."https://zbmath.org/authors/?q=ai:pakhare.sumit-s"Gade, Prashant M."https://zbmath.org/authors/?q=ai:gade.prashant-m(no abstract)Predicting the emergence of multistability in a monoparametric PWL systemhttps://zbmath.org/1544.700232024-11-01T15:51:55.949586Z"Echenausía-Monroy, J. L."https://zbmath.org/authors/?q=ai:echenausia-monroy.j-l"Jafari, S."https://zbmath.org/authors/?q=ai:jafari.sajad"Huerta-Cuellar, G."https://zbmath.org/authors/?q=ai:huerta-cuellar.guillermo"Gilardi-Velázquez, H. E."https://zbmath.org/authors/?q=ai:gilardi-velazquez.hector-eduardo(no abstract)Contact interactions and gamma convergencehttps://zbmath.org/1544.810352024-11-01T15:51:55.949586Z"Dell'Antonio, Gianfausto"https://zbmath.org/authors/?q=ai:dellantonio.gian-faustoSummary: We study contact interactions, a generalization of Albeverio's point interactions. There are two types of contact interactions, weak and strong; the last type occurs only in a three particle system. Strong contact leads to systems that have an infinite number of bound states with eigenvalues that decrease with a scaling law. We prove that in both the strong and the weak contact cases the hamiltonians are strong resolvent limits of hamiltonians with potentials with support that vanishes with a given scaling law while the \(L^1\) norm remains constant. In the weak contact case, the approximating hamiltonians must have a zero energy resonance. As applications we describe Bose-Einstein condensation in the low and high density regimes, the Fermi sea in solid state physics and the ground state of Nelson's polaron.
For the entire collection see [Zbl 1515.81020].Average entropy and asymptoticshttps://zbmath.org/1544.810482024-11-01T15:51:55.949586Z"Barron, Tatyana"https://zbmath.org/authors/?q=ai:barron.tatyana"Saikia, Manimugdha"https://zbmath.org/authors/?q=ai:saikia.manimugdhaAuthors' abstract: We determine the \(N \to \infty\) asymptotics of the expected value of entanglement entropy for pure states in \(H_{1, N} \otimes H_{2, N}\), where \(H_{1, N}\) and \(H_{2, N}\) are the spaces of holomorphic sections of the \(N\)-th tensor powers of hermitian ample line bundles on compact complex manifolds.
Reviewer: Jesus Muciño Raymundo (Morelia)Quantum integrability and chaos in a periodic Toda lattice with balanced loss-gainhttps://zbmath.org/1544.810592024-11-01T15:51:55.949586Z"Ghosh, Supriyo"https://zbmath.org/authors/?q=ai:ghosh.supriyo.1|ghosh.supriyo|ghosh.supriyo.2"Ghosh, Pijush K."https://zbmath.org/authors/?q=ai:ghosh.pijush-k|ghosh.pijush-kanti(no abstract)Emergence of central extension of Kac-Moody algebra in quantum integrable modelshttps://zbmath.org/1544.810752024-11-01T15:51:55.949586Z"Bhattacharya, Gautam"https://zbmath.org/authors/?q=ai:bhattacharya.gautam"Chau, Ling-Lie"https://zbmath.org/authors/?q=ai:chau.linglieSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].Quantum decoherence via Chernoff averageshttps://zbmath.org/1544.810862024-11-01T15:51:55.949586Z"Kalmetev, R. Sh."https://zbmath.org/authors/?q=ai:kalmetev.rustem-shainurovich"Orlov, Yu. N."https://zbmath.org/authors/?q=ai:orlov.yurii-nikolaevich"Sakbaev, V. Zh."https://zbmath.org/authors/?q=ai:sakbaev.vsevolod-zhSummary: In this paper we study Chernoff averages for time evolution operators. We consider the time evolution of quantum oscillator defined by compositions of random affine phase-space transformations and the diffusion limit of such compositions in the sense of Feynman-Chernoff iterations. The Fokker-Planck equation for the evolution of quasi-probability distribution functions is provided and the problem of decoherence of quantum states in interference experiments is numerically investigated.Yang-Baxter algebras of dynamical charges in the chiral Gross-Neveu modelhttps://zbmath.org/1544.811062024-11-01T15:51:55.949586Z"Eichenherr, H."https://zbmath.org/authors/?q=ai:eichenherr.haraldSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].Self-dual monopoles and caloronshttps://zbmath.org/1544.811082024-11-01T15:51:55.949586Z"Nahm, W."https://zbmath.org/authors/?q=ai:nahm.wernerSee the review of the entire volume [Zbl 0597.22002].
For the entire collection see [Zbl 0597.22002].Universal 1-loop divergences for integrable sigma modelshttps://zbmath.org/1544.811172024-11-01T15:51:55.949586Z"Levine, Nat"https://zbmath.org/authors/?q=ai:levine.natSummary: We present a simple, new method for the 1-loop renormalization of integrable \(\sigma\)-models. By treating equations of motion and Bianchi identities on an equal footing, we derive `universal' formulae for the 1-loop on-shell divergences, generalizing case-by-case computations in the literature. Given a choice of poles for the classical Lax connection, the divergences take a theory-independent form in terms of the Lax currents (the residues of the poles), assuming a `completeness' condition on the zero-curvature equations. We compute these divergences for a large class of theories with simple poles in the Lax connection. We also show that \(\mathbb{Z}_T\) coset models of `pure-spinor' type and their recently constructed \(\eta\)- and \(\lambda\)-deformations are 1-loop renormalizable, and 1-loop scale-invariant when the Killing form vanishes.Spectral curves and \(\mathcal{W}\)-representations of matrix modelshttps://zbmath.org/1544.811472024-11-01T15:51:55.949586Z"Mironov, A."https://zbmath.org/authors/?q=ai:mironov.andrei-d"Morozov, A."https://zbmath.org/authors/?q=ai:morozov.alexei-yurievichSummary: We explain how the spectral curve can be extracted from the \(\mathcal{W}\)-representation of a matrix model. It emerges from the part of the \(\mathcal{W}\)-operator, which is linear in time-variables. A possibility of extracting the spectral curve in this way is important because there are models where matrix integrals are not yet available, and still they possess all their important features. We apply this reasoning to the family of WLZZ models and discuss additional peculiarities which appear for the non-negative value of the family parameter \(n\), when the model depends on additional couplings (dual times). In this case, the relation between topological and \(1/N\) expansions is broken. On the other hand, all the WLZZ partition functions are \(\tau\)-functions of the Toda lattice hierarchy, and these models also celebrate the superintegrability properties.The ordered exponential representation of GKM using the \(W_{1 + \infty}\) operatorhttps://zbmath.org/1544.811502024-11-01T15:51:55.949586Z"Wang, Gehao"https://zbmath.org/authors/?q=ai:wang.gehaoSummary: The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an \(r\)-reduced tau-function that governs the \(r\)-spin intersection numbers. In this paper, we present an ordered exponential representation of monomial GKM in terms of the \(W_{1 + \infty}\) operators that preserves the KP integrability. In fact, this representation is naturally the solution of a \(W_{1 + \infty}\) constraint that uniquely determines the tau-function. Furthermore, we show that, for the cases of Kontsevich-Witten and generalized BGW tau-functions, their \(W_{1 + \infty}\) representations can be reduced to their cut-and-join representations under the reduction of the even time independence and Virasoro constraints.Deforming the ODE/IM correspondence with \(\mathrm{T}\overline{\mathrm{T}}\)https://zbmath.org/1544.811552024-11-01T15:51:55.949586Z"Aramini, Fabrizio"https://zbmath.org/authors/?q=ai:aramini.fabrizio"Brizio, Nicolò"https://zbmath.org/authors/?q=ai:brizio.nicolo"Negro, Stefano"https://zbmath.org/authors/?q=ai:negro.stefano"Tateo, Roberto"https://zbmath.org/authors/?q=ai:tateo.robertoSummary: The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after \(\mathrm{T}\overline{\mathrm{T}}\) perturbation on both sides of the correspondence. In particular, we prove that the deformed Lax pair of the sinh-Gordon model, obtained from the unperturbed one through a dynamical change of coordinates, leads to the same Burgers-type equation governing the quantum spectral flow induced by \(\mathrm{T}\overline{\mathrm{T}}\). Our main conclusions have general validity, as the analysis may be easily adapted to all the known ODE/IM examples involving integrable quantum field theories.Integrable crosscaps in classical sigma modelshttps://zbmath.org/1544.811652024-11-01T15:51:55.949586Z"Gombor, Tamas"https://zbmath.org/authors/?q=ai:gombor.tamasSummary: We study the integrable boundaries and crosscaps of classical sigma models. We show that there exists a classical analog of the integrability condition and KT-relation of the boundary and crosscap states of quantum spin chains. We also classify the integrable crosscaps for various sigma models including examples which are relevant in the AdS/CFT correspondence at strong coupling.Higher dimensional CFTs as 2D conformally-equivariant topological field theorieshttps://zbmath.org/1544.811822024-11-01T15:51:55.949586Z"de Mello Koch, Robert"https://zbmath.org/authors/?q=ai:de-mello-koch.robert"Ramgoolam, Sanjaye"https://zbmath.org/authors/?q=ai:ramgoolam.sanjayeSummary: Two and three-point functions of primary fields in four dimensional CFT have simple space-time dependences factored out from the combinatoric structure which enumerates the fields and gives their couplings. This has led to the formulation of two dimensional topological field theories with \(SO(4, 2)\) equivariance which are conjectured to be equivalent to higher dimensional conformal field theories. We review this CFT4/TFT2 construction in the simplest possible setting of a free scalar field, which gives an algebraic construction of the correlators in terms of an infinite dimensional \(so(4, 2)\) equivariant algebra with finite dimensional subspaces at fixed scaling dimension. Crossing symmetry of the CFT4 is related to associativity of the algebra. This construction is then extended to describe perturbative CFT4, by making use of deformed co-products. Motivated by the Wilson-Fisher CFT we outline the construction of \(\mathrm{U}(so(d,2))\) equivariant TFT2 for non-integer \(d\), in terms of diagram algebras and their representations.
For the entire collection see [Zbl 1515.17004].Octonionic Clifford algebra for the internal space of the standard modelhttps://zbmath.org/1544.812232024-11-01T15:51:55.949586Z"Todorov, Ivan"https://zbmath.org/authors/?q=ai:todorov.ivan-t|todorov.ivan-gSummary: We explore the \({\mathbb{Z}}_2\) graded product \(C{\ell}_{10} = C{\ell}_4 \, {\widehat{\otimes}} \, C{\ell}_6\) as a finite internal space algebra of the Standard Model of particle physics. The gamma matrices generating \(C{\ell}_{10}\) are expressed in terms of left multiplication by the imaginary octonion units and the Pauli matrices. The subgroup of Spin(10) that fixes an imaginary unit (and thus allows to write \({\mathbb{O}} = {\mathbb{C}} \oplus{\mathbb{C}}^3\) expressing the quark-lepton splitting) is the Pati-Salam group \(G_\mathrm{PS} = Spin (4) \times Spin (6) / {\mathbb{Z}}_2 \subset Spin (10)\). If we identify the preserved imaginary unit with the \(C{\ell}_6\) pseudoscalar \(\omega_6 = \gamma_1 \cdots \gamma_6\), \(\omega_6^2 = -1\), then \(\mathcal{P} = \frac{1}{2} (1 - i\omega_6)\) will be the projector on the extended particle subspace, including the right-handed (sterile) neutrino. We express the generators of \(C{\ell}_4\) and \(C{\ell}_6\) in terms of fermionic oscillators \(a_{\alpha}\), \(a_{\alpha}^*\), \(\alpha = 1,2\) and \(b_j\), \(b_j^*\), \(j = 1,2,3\) describing flavour and colour, respectively. The internal space observables belong to the Jordan subalgebra of hermitian elements of the complexified Clifford algebra \({\mathbb{C}} \otimes C{\ell}_{10}\) which commute with the weak hypercharge \(\frac{1}{2} Y = \frac{1}{3} \sum_{j=1}^3 b_j^* b_j - \frac{1}{2} \sum_{\alpha = 1}^2 a_{\alpha}^* a_{\alpha}\). We only distinguish particles from antiparticles if they have different eigenvalues of \(Y\). Thus the sterile neutrino and antineutrino (both with \(Y=0)\) are allowed to mix into Majorana neutrinos. Restricting \(C{\ell}_{10}\) to the particle subspace, which consists of leptons with \(Y < 0\) and quarks, allows a natural definition of the Higgs field \(\varPhi\), the scalar of Quillen's superconnection, as an element of \(C{\ell}_4^1\), the odd part of the first factor in \(C{\ell}_{10}\). As an application we express the ratio \(\frac{m_H}{m_W}\) of the Higgs and the \(W\)-boson masses in terms of the cosine of the \textit{theoretical} Weinberg angle.
For the entire collection see [Zbl 1515.17004].Acceleration of solar wind particles due to inertial Alfvén waveshttps://zbmath.org/1544.850012024-11-01T15:51:55.949586Z"Batool, Kiran"https://zbmath.org/authors/?q=ai:batool.kiran"Khan, Imran A."https://zbmath.org/authors/?q=ai:khan.imran-a.1"Shamir, M."https://zbmath.org/authors/?q=ai:shamir.maoz|shamir.m-farasat"Kabir, Abdul"https://zbmath.org/authors/?q=ai:kabir.abdul"Ayaz, S."https://zbmath.org/authors/?q=ai:ayaz.sedat(no abstract)Macro-financial dynamics: theories, empirical methods, and time scaleshttps://zbmath.org/1544.913062024-11-01T15:51:55.949586Z"Proaño, Christian R."https://zbmath.org/authors/?q=ai:proano.christian-r"Virla, Leonardo Quero"https://zbmath.org/authors/?q=ai:virla.leonardo-queroSummary: While the orthodox neoclassical view sees the financial system as a mere reflection of the real side of the economy, many researchers -- most prominently, Hyman Minsky -- have stressed the potential instability of financial fluctuations and their pervasive effects on the real economic sector. This chapter reviews the literature on cyclical dynamics of financial aggregates, from the pioneer financial fragility theory of Hyman Minsky to the subsequent empirical work on the financial cycle that gained popularity over the last decade. We put special emphasis on outlining the different methodological approaches, estimation frameworks, and the complex interactions between heterogenous financial market agents and the macroeconomy.
For the entire collection see [Zbl 1537.37001].Homeostasis in networks with multiple inputshttps://zbmath.org/1544.920702024-11-01T15:51:55.949586Z"Madeira, João Luiz de Oliveira"https://zbmath.org/authors/?q=ai:madeira.joao-luiz-de-oliveira"Antoneli, Fernando"https://zbmath.org/authors/?q=ai:antoneli.fernando-junSummary: Homeostasis, also known as adaptation, refers to the ability of a system to counteract persistent external disturbances and tightly control the output of a key observable. Existing studies on homeostasis in network dynamics have mainly focused on `perfect adaptation' in deterministic single-input single-output networks where the disturbances are scalar and affect the network dynamics via a pre-specified input node. In this paper we provide a full classification of all possible network topologies capable of generating infinitesimal homeostasis in arbitrarily large and complex multiple inputs networks. Working in the framework of `infinitesimal homeostasis' allows us to make no assumption about how the components are interconnected and the functional form of the associated differential equations, apart from being compatible with the network architecture. Remarkably, we show that there are just three distinct `mechanisms' that generate infinitesimal homeostasis. Each of these three mechanisms generates a rich class of well-defined network topologies -- called \textit{homeostasis subnetworks}. More importantly, we show that these classes of homeostasis subnetworks provides a topological basis for the classification of `homeostasis types': the full set of all possible multiple inputs networks can be uniquely decomposed into these special homeostasis subnetworks. We illustrate our results with some simple abstract examples and a biologically realistic model for the co-regulation of calcium (Ca) and phosphate (\(\mathrm{PO}_{4}\)) in the rat. Furthermore, we identify a new phenomenon that occurs in the multiple input setting, that we call \textit{homeostasis mode interaction}, in analogy with the well-known characteristic of multiparameter bifurcation theory.Supercritical Neimark-Sacker bifurcation and hybrid control in a discrete-time glycolytic oscillator modelhttps://zbmath.org/1544.920752024-11-01T15:51:55.949586Z"Khan, A. Q."https://zbmath.org/authors/?q=ai:khan.abdul-qadeer"Abdullah, E."https://zbmath.org/authors/?q=ai:abdullah.enas-fadhil|abdullah.e-j"Ibrahim, Tarek F."https://zbmath.org/authors/?q=ai:ibrahim.tarek-fawziSummary: We study the local dynamical properties, Neimark-Sacker bifurcation, and hybrid control in a glycolytic oscillator model in the interior of \(\mathbb{R}_+^2\). It is proved that, for all parametric values, \(P_{x y}^+ \left(\alpha / \left(\beta + \alpha^2\right), \alpha\right)\) is the unique positive equilibrium point of the glycolytic oscillator model. Further local dynamical properties along with different topological classifications about the equilibrium \(P_{x y}^+ \left(\alpha / \left(\beta + \alpha^2\right), \alpha\right)\) have been investigated by employing the method of linearization. Existence of prime period and periodic points of the model under consideration are also investigated. It is proved that, about the fixed point \(P_{x y}^+ \left(\alpha / \left(\beta + \alpha^2\right), \alpha\right)\), the discrete-time glycolytic oscillator model undergoes no bifurcation, except Neimark-Sacker bifurcation. A further hybrid control strategy is applied to control Neimark-Sacker bifurcation in the discrete-time model. Finally, theoretical results are verified numerically.Bifurcation analysis of a modified Leslie-Gower predator-prey systemhttps://zbmath.org/1544.921362024-11-01T15:51:55.949586Z"Jia, Xintian"https://zbmath.org/authors/?q=ai:jia.xintian"Huang, Kunlun"https://zbmath.org/authors/?q=ai:huang.kunlun"Li, Cuiping"https://zbmath.org/authors/?q=ai:li.cuiping(no abstract)Stability and bifurcation analysis of Bazykin's model with Holling I functional response and Allee effecthttps://zbmath.org/1544.921422024-11-01T15:51:55.949586Z"Li, Danyang"https://zbmath.org/authors/?q=ai:li.danyang"Liu, Hua"https://zbmath.org/authors/?q=ai:liu.hua.2|liu.hua.1"Han, Xiaotao"https://zbmath.org/authors/?q=ai:han.xiaotao"Lin, Xiaofen"https://zbmath.org/authors/?q=ai:lin.xiaofen"Wei, Yumei"https://zbmath.org/authors/?q=ai:wei.yumei(no abstract)Dynamics of a discrete Lotka-Volterra information diffusion modelhttps://zbmath.org/1544.921432024-11-01T15:51:55.949586Z"Li, Mingshan"https://zbmath.org/authors/?q=ai:li.mingshan"Xie, Naiming"https://zbmath.org/authors/?q=ai:xie.naiming"Zhang, Ran"https://zbmath.org/authors/?q=ai:zhang.ran.1|zhang.ran.4|zhang.ran"Huang, Xiaojun"https://zbmath.org/authors/?q=ai:huang.xiaojun.1|huang.xiaojun(no abstract)Bifurcation and chaos of a discrete predator-prey model with Crowley-Martin functional response incorporating proportional prey refugehttps://zbmath.org/1544.921512024-11-01T15:51:55.949586Z"Santra, P. K."https://zbmath.org/authors/?q=ai:santra.prasun-kumar"Mahapatra, G. S."https://zbmath.org/authors/?q=ai:mahapatra.ghanshaym-singha"Phaijoo, G. R."https://zbmath.org/authors/?q=ai:phaijoo.ganga-ramSummary: The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley-Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark-Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.Estimation of spreading speeds and travelling waves for the lattice pioneer-climax competition systemhttps://zbmath.org/1544.921532024-11-01T15:51:55.949586Z"Song, Haifeng"https://zbmath.org/authors/?q=ai:song.haifeng"Zhang, Yuxiang"https://zbmath.org/authors/?q=ai:zhang.yuxiangSummary: This paper concerns the invasion dynamics of the lattice pioneer-climax competition model with parameter regions in which the system is non-monotone. We estimate the spreading speeds and establish appropriate conditions under which the spreading speeds are linearly selected. Moreover, the existence of travelling waves is determined by constructing suitable upper and lower solutions. It shows that the spreading speed coincides with the minimum wave speed of travelling waves if the diffusion rate of the invasive species is larger or equal to that of the native species. Our results are new to estimate the spreading speed of non-monotone lattice pioneer-climax systems, and the techniques developed in this work can be used to study the invasion dynamics of the pioneer-climax system with interaction delays, which could extend the results in the literature. The analysis replies on the construction of auxiliary systems, upper and lower solutions, and the monotone dynamical system approach.Dynamics of a delayed predator-prey model with prey refuge, Allee effect and fear effecthttps://zbmath.org/1544.921572024-11-01T15:51:55.949586Z"Wei, Zhen"https://zbmath.org/authors/?q=ai:wei.zhen.1|wei.zhen"Chen, Fengde"https://zbmath.org/authors/?q=ai:chen.fengde(no abstract)Stationary distribution and ergodicity of a stochastic multi-species model with Holling type II response functionhttps://zbmath.org/1544.921582024-11-01T15:51:55.949586Z"Xu, Libai"https://zbmath.org/authors/?q=ai:xu.libai"Zhao, Yanyan"https://zbmath.org/authors/?q=ai:zhao.yanyanSummary: In this paper, we consider a stochastic multi-species model with the Holling type II functional response, which includes the stochastic competition model, the stochastic mutualism model, and the stochastic hybrid model of competition and mutualism. Sufficient conditions for the stationary distribution and ergodicity of the model are established. We support our analytical findings through extensive simulation studies. We show that under relatively small noise, the model has a stationary distribution and ergodicity, while the relatively large noise leads to the non-persistent and non-stationary distribution of the model through the numerical simulation studies of three species.Sustainable management of predatory fish affected by an Allee effect through marine protected areas and taxationhttps://zbmath.org/1544.921592024-11-01T15:51:55.949586Z"Yuan, Xiaoyue"https://zbmath.org/authors/?q=ai:yuan.xiaoyue"Liu, Wenjun"https://zbmath.org/authors/?q=ai:liu.wenjun|liu.wenjun-j"Lv, Guangying"https://zbmath.org/authors/?q=ai:lv.guangying"Moussaoui, Ali"https://zbmath.org/authors/?q=ai:moussaoui.ali"Auger, Pierre"https://zbmath.org/authors/?q=ai:auger.pierre-mSummary: Ecological balance and stable economic development are crucial for the fishery. This study proposes a predator-prey system for marine communities, where the growth of predators follows the Allee effect and takes into account the rapid fluctuations in resource prices caused by supply and demand. The system predicts the existence of catastrophic equilibrium, which may lead to the extinction of prey, consequently leading to the extinction of predators, but fishing efforts remain high. Marine protected areas are established near fishing areas to avoid such situations. Fish migrate rapidly between these two areas and are only harvested in the nonprotected areas. A three-dimensional simplified model is derived by applying variable aggregation to describe the variation of global variables on a slow time scale. To seek conditions to avoid species extinction and maintain sustainable fishing activities, the existence of positive equilibrium points and their local stability are explored based on the simplified model. Moreover, the long-term impact of establishing marine protected areas and levying taxes based on unit catch on fishery dynamics is studied, and the optimal tax policy is obtained by applying Pontryagin's maximum principle. The theoretical analysis and numerical examples of this study demonstrate the comprehensive effectiveness of increasing the proportion of marine protected areas and controlling taxes on the sustainable development of fishery.Modeling and stability analysis of the dynamics of malaria disease transmission with some control strategieshttps://zbmath.org/1544.921672024-11-01T15:51:55.949586Z"Ayalew, Alemzewde"https://zbmath.org/authors/?q=ai:ayalew.alemzewde"Molla, Yezbalem"https://zbmath.org/authors/?q=ai:molla.yezbalem"Woldegbreal, Amsalu"https://zbmath.org/authors/?q=ai:woldegbreal.amsalu(no abstract)Oscillating behavior of a compartmental model with retarded noisy dynamic infection ratehttps://zbmath.org/1544.921692024-11-01T15:51:55.949586Z"Bestehorn, Michael"https://zbmath.org/authors/?q=ai:bestehorn.michael"Michelitsch, Thomas M."https://zbmath.org/authors/?q=ai:michelitsch.thomas-m(no abstract)Dimension reduction in higher-order contagious phenomenahttps://zbmath.org/1544.921832024-11-01T15:51:55.949586Z"Ghosh, Subrata"https://zbmath.org/authors/?q=ai:ghosh.subrata"Khanra, Pitambar"https://zbmath.org/authors/?q=ai:khanra.pitambar"Kundu, Prosenjit"https://zbmath.org/authors/?q=ai:kundu.prosenjit"Ji, Peng"https://zbmath.org/authors/?q=ai:ji.peng"Ghosh, Dibakar"https://zbmath.org/authors/?q=ai:ghosh.dibakar"Hens, Chittaranjan"https://zbmath.org/authors/?q=ai:hens.chittaranjan(no abstract)Mathematical modeling of coccidiosis dynamics in chickens with some control strategieshttps://zbmath.org/1544.921912024-11-01T15:51:55.949586Z"Liana, Yustina A."https://zbmath.org/authors/?q=ai:liana.yustina-a"Swai, Mary C."https://zbmath.org/authors/?q=ai:swai.mary-c(no abstract)Global threshold analysis of an age-space structured disease model with relapsehttps://zbmath.org/1544.921942024-11-01T15:51:55.949586Z"Lyu, Guoyang"https://zbmath.org/authors/?q=ai:lyu.guoyang"Guo, Yutong"https://zbmath.org/authors/?q=ai:guo.yutong"Wang, Jinliang"https://zbmath.org/authors/?q=ai:wang.jinliangSummary: In this paper, an age-space structured disease model with age-dependent relapse rate is investigated. We first prove the well-posedness of the model including the existence and uniqueness of the solution, positivity, and boundedness. By performing the Laplace transformation to renewal equation, we derive the next generation operator, whose spectral radius is defined as the basic reproduction number. By checking the distribution of the roots of the characteristic equation, exploring the strong persistence property of the solution and designing the Lyapunov functionals, we establish the local and global dynamics of the model.A complex dynamic of an eco-epidemiological mathematical model with migrationhttps://zbmath.org/1544.921992024-11-01T15:51:55.949586Z"Savadogo, Assane"https://zbmath.org/authors/?q=ai:savadogo.assane"Sangaré, Boureima"https://zbmath.org/authors/?q=ai:sangare.boureima"Ouedraogo, Wendkouni"https://zbmath.org/authors/?q=ai:ouedraogo.wendkouni(no abstract)Modeling and analysis of Fasciola hepatica disease transmissionhttps://zbmath.org/1544.922112024-11-01T15:51:55.949586Z"Yihunie, Dagnaw Tantie"https://zbmath.org/authors/?q=ai:yihunie.dagnaw-tantie"Mugisha, Joseph Y. T."https://zbmath.org/authors/?q=ai:mugisha.joseph-y-t"Gebru, Dawit Melese"https://zbmath.org/authors/?q=ai:gebru.dawit-melese"Alemneh, Haileyesus Tessema"https://zbmath.org/authors/?q=ai:alemneh.haileyesus-tessema(no abstract)Permanence for continuous-time competitive Kolmogorov systems via the carrying simplexhttps://zbmath.org/1544.922182024-11-01T15:51:55.949586Z"Niu, Lei"https://zbmath.org/authors/?q=ai:niu.lei"Song, Yuheng"https://zbmath.org/authors/?q=ai:song.yuhengSummary: In this paper we study the permanence and impermanence for continuous-time competitive Kolmogorov systems via the carrying simplex. We first give an extension to attractors of \textit{V. Hutson}'s result [Monatsh. Math. 98, 267--275 (1984; Zbl 0542.34043)] on the existence of repellors in continuous-time dynamical systems that have found wide use in the study of permanence via average Lyapunov functions. We then give a general criterion for the stability of the boundary of carrying simplex for competitive Kolmogorov systems of differential equations, which determines the permanence and impermanence of such systems. Based on the criterion, we present a complete classification of the permanence and impermanence in terms of inequalities on parameters for all three-dimensional competitive systems which have linearly determined nullclines. The results are applied to many classical models in population dynamics including the Lotka-Volterra system, Gompertz system, Leslie-Gower system and Ricker system.Stability via closure relations with applications to dissipative and port-Hamiltonian systemshttps://zbmath.org/1544.936642024-11-01T15:51:55.949586Z"Glück, Jochen"https://zbmath.org/authors/?q=ai:gluck.jochen"Jacob, Birgit"https://zbmath.org/authors/?q=ai:jacob.birgit"Meyer, Annika"https://zbmath.org/authors/?q=ai:meyer.annika"Wyss, Christian"https://zbmath.org/authors/?q=ai:wyss.christian"Zwart, Hans"https://zbmath.org/authors/?q=ai:zwart.hans-jSummary: We consider differential operators \(A\) that can be represented by means of a so-called closure relation in terms of a simpler operator \(A_{\mathrm{ext}}\) defined on a larger space. We analyse how the spectral properties of \(A\) and \(A_{\mathrm{ext}}\) are related and give sufficient conditions for exponential stability of the semigroup generated by \(A\) in terms of the semigroup generated by \(A_{\mathrm{ext}}\). As applications we study the long-term behaviour of a coupled wave-heat system on an interval, parabolic equations on bounded domains that are coupled by matrix-valued potentials, and of linear infinite-dimensional port-Hamiltonian systems with dissipation on an interval.Gradient flows for regularized stochastic control problemshttps://zbmath.org/1544.938522024-11-01T15:51:55.949586Z"Šiška, David"https://zbmath.org/authors/?q=ai:siska.david"Szpruch, Łukasz"https://zbmath.org/authors/?q=ai:szpruch.lukaszSummary: This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalized by the relative entropy. We identify a suitable metric space on which we construct a gradient flow for the measure-valued control process, in the set of admissible controls, along which the cost functional is guaranteed to decrease. It is shown that any invariant measure of this gradient flow satisfies the Pontryagin optimality principle. If the problem we work with is sufficiently convex, the gradient flow converges exponentially fast. Furthermore, the optimal measure-valued control process admits a Bayesian interpretation, which means that one can incorporate prior knowledge when solving such stochastic control problems. This work is motivated by a desire to extend the theoretical underpinning for the convergence of stochastic gradient type algorithms widely employed in the reinforcement learning community to solve control problems.Reducing the dynamical degradation of digital chaotic maps with time-delay linear feedback and parameter perturbationhttps://zbmath.org/1544.940652024-11-01T15:51:55.949586Z"Liu, Bocheng"https://zbmath.org/authors/?q=ai:liu.bocheng"Xiang, Hongyue"https://zbmath.org/authors/?q=ai:xiang.hongyue"Liu, Lingfeng"https://zbmath.org/authors/?q=ai:liu.lingfengSummary: Digital chaotic maps are not secure enough for cryptographic applications due to their dynamical degradation. In order to improve their dynamics, in this paper, a novel method with time-delay linear feedback and parameter perturbation is proposed. The delayed state variable is used to construct the linear feedback function and parameter perturbation function. This method is universal for all different digital chaotic maps. Here, two examples are presented: one is 1D logistic map and the other is 2D Baker map. To show the effectiveness of this method, we take some numerical experiments, including trajectory and phase space analysis, correlation analysis, period analysis, and complexity analysis. All the numerical results prove that the method can greatly improve the dynamics of digital chaotic maps and is quite competitive with other proposed methods. Furthermore, a simple pseudorandom bit generator (PRBG) based on digital Baker map is proposed to show its potential application. The proposed PRBG is completely constructed by the digital chaotic map, without any other complex operations. Several numerical results indicate that this PRBG has good randomness and high complexity level.Coexistence of hidden attractors in the smooth cubic Chua's circuit with two stable equilibriahttps://zbmath.org/1544.943032024-11-01T15:51:55.949586Z"Ahmad, Irfan"https://zbmath.org/authors/?q=ai:ahmad.irfan"Srisuchinwong, Banlue"https://zbmath.org/authors/?q=ai:srisuchinwong.banlue"Usman Jamil, Muhammad"https://zbmath.org/authors/?q=ai:usman-jamil.muhammad(no abstract)In-depth analysis of smooth and nonsmooth bifurcations for an open-loop boost converter feeding constant power loads in discontinuous conduction modehttps://zbmath.org/1544.943062024-11-01T15:51:55.949586Z"Benadero, Luis"https://zbmath.org/authors/?q=ai:benadero.luis"El Aroudi, Abdelali"https://zbmath.org/authors/?q=ai:el-aroudi.abdelali"Martinez-Salamero, Luis"https://zbmath.org/authors/?q=ai:martinez-salamero.luis"Tse, Chi K."https://zbmath.org/authors/?q=ai:tse.chi-kong(no abstract)