Recent zbMATH articles in MSC 34https://zbmath.org/atom/cc/342023-01-20T17:58:23.823708ZWerkzeugThe \(\ast \)-Markov equation for Laurent polynomialshttps://zbmath.org/1500.110272023-01-20T17:58:23.823708Z"Cotti, Giordano"https://zbmath.org/authors/?q=ai:cotti.giordano"Varchenko, Alexander"https://zbmath.org/authors/?q=ai:varchenko.alexander-nThe classical Markov equation is the Diophantine equation
\[
a^2+b^2+c^2-abc=0,
\]
where \(a,b,c \in \mathbb{Z}\) with initial solution \((3,3,3)\). In this paper, the authors considers a generalization of the Markov equation called the \(\ast\)-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which appears as an equivalent analog of the classical Markov equation for integers.
Denote \(z=(z_1,z_2,z_3)\), \(s=(s_1,s_2,s_3)\), and let \(\mathbb{Z}[z^{\pm 1}]^{\vartheta_3}\) be the ring of symmetric Laurent polynomials in \(z\) with integer coefficients, then the isomorphism
\[
\mathbb{Z}[z^{\pm 1}]^{\vartheta_3} \cong \mathbb{Z}[s_1,s_2,s_3^{\pm 1}]
\]
is defined by sending
\[
(z_1 + z_2 + z_3, z_1z_2 + z_1z_3 + z_2z_3,z_1z_2z_3) \longrightarrow (s_1, s_2, s_3).
\]
The \(\ast\)-Markov equation is the equation
\[
aa^\ast+bb^\ast+cc^\ast-abc=\frac{3s_1s_2-s_1^3}{s_3},
\]
where \(a,b,c \in \mathbb{Z}[s_1,s_2,s_3^{\pm 1}]\) and \((s_1, \frac{s_1}{s_3}, s_1)\) represents the initial solution. Moreover, they study how the properties of the Markov equation and its solutions are reflected in the properties of the \(\ast\)-Markov equation and its solutions. More precisely, the \(\ast\)-group and its subgroups are defined, and the Markov and extended Markov trees are introduced. Furthermore, the notion of an admissible triple of Laurent polynomials, the notion of a reduced polynomial presentation of a Markov triple, and the notion of a \(\ast\)-Markov polynomial are introduced. The most important result of this paper says that a Markov triple has a unique reduced polynomial presentation.
Also, the authors define the following six decorated infinite planar binary trees: the \(\ast\)-Markov polynomial tree, 2-vector tree, matrix tree, deviation tree, Markov tree, and Euclid tree. Then, they discuss the interrelations between the trees and study the problem of the asymptotics of the decorations along the infinite paths from the root of the tree to infinity. They also introduce they odd \(\ast\)-Fibonacci and the odd \(\ast\)-Pell polynomials with discussing their properties. Last but not least, they construct actions of the \(\ast\)-Markov group on the spaces \(\mathbb{C}^6\) and \(\mathbb{C}^5\) and a map \(\mathbb{F}: \mathbb{C}^6 \longrightarrow \mathbb{C}^5\) commuting with the actions. Finally, they establish \(\ast\)-analogs of the Horowitz Theorem on \(\mathbb{C}^6\) and \(\mathbb{C}^5\).
Reviewer: Hayder Hashim (Kufa)An efficient fractional integration operational matrix of the Chebyshev wavelets and its applications for multi-order fractional differential equationshttps://zbmath.org/1500.260042023-01-20T17:58:23.823708Z"Aruldoss, R."https://zbmath.org/authors/?q=ai:aruldoss.r"Devi, R. Anusuya"https://zbmath.org/authors/?q=ai:anusuya-devi.rThe authors deal with a technique by an operational matrix of fractional order integration of Chebyshev wavelets to solve multi-order fractional differential equations. The most important point in this method is that the introduced matrix is sparse and then the computational complexity is decreased.
The work is well written, well organized, proofs are accurate and the results are suitable for numerous applications in mathematical modeling. In addition, to show the efficiency of the introduced matrix some numerical examples are given.
Reviewer: Niloufar Seddighi (Maragheh)Existence result for a problem involving \(\psi \)-Riemann-Liouville fractional derivative on unbounded domainhttps://zbmath.org/1500.260052023-01-20T17:58:23.823708Z"Benia, Kheireddine"https://zbmath.org/authors/?q=ai:benia.kheireddine"Beddani, Moustafa"https://zbmath.org/authors/?q=ai:beddani.moustafa"Fečkan, Michal"https://zbmath.org/authors/?q=ai:feckan.michal"Hedia, Benaouda"https://zbmath.org/authors/?q=ai:hedia.benaoudaSummary: This paper deals with the the existence of solution sets and its topological structure for a fractional differential equation with \(\psi \)-Riemann-Liouville fractional derivative on \((0, \infty)\) in a special Banach space. Our approach is based on a fixed point theorem for Meir-Keeler condensing operators combined with measure of non-compactness. An example is given to illustrate our approach.Single-spike solutions to the 1D shadow Gierer-Meinhardt problemhttps://zbmath.org/1500.340012023-01-20T17:58:23.823708Z"Iuorio, Annalisa"https://zbmath.org/authors/?q=ai:iuorio.annalisa"Kuehn, Christian"https://zbmath.org/authors/?q=ai:kuhn.christianSummary: A fundamental example of reaction-diffusion system exhibiting Turing-type pattern formation is the Gierer-Meinhardt system, which reduces to the shadow Gierer-Meinhardt problem in a suitable singular limit. Thanks to its applicability in a large range of biological applications, this singularly perturbed problem has been widely studied in the last few decades via rigorous, asymptotic, and numerical methods. However, standard matched asymptotics methods do not apply [\textit{W.-M. Ni}, Notices Am. Math. Soc. 45, No. 1, 9--18 (1998; Zbl 0917.35047); \textit{J. Wei}, Proc. R. Soc. Edinb., Sect. A, Math. 128, No. 4, 849--874 (1998; Zbl 0944.35021)], and therefore analytical expressions for single spike solutions are generally lacking.
By introducing an ansatz based on generalized hyperbolic functions, we determine exact radially symmetric solutions to the one-dimensional shadow Gierer-Meinhardt problem for any \(1 < p < \infty \), representing both inner and boundary spike solutions depending on the location of the peak. Our approach not only confirms numerical results existing in literature, but also provides guidance for tackling extensions of the shadow Gierer-Meinhardt problem based on different boundary conditions (e.g. mixed) and/or \(n\)-dimensional domains.Lax representation and a quadratic rational first integral for second-order differential equations with cubic nonlinearityhttps://zbmath.org/1500.340022023-01-20T17:58:23.823708Z"Sinelshchikov, Dmitry I."https://zbmath.org/authors/?q=ai:sinelshchikov.dmitry-i"Guha, Partha"https://zbmath.org/authors/?q=ai:guha.partha"Choudhury, A. Ghose"https://zbmath.org/authors/?q=ai:ghose-choudhury.anindyaSummary: In this paper we give a Lax formulation for a family of non-autonomous second-order differential equations of the type \(y_{zz}+a_3(z,y)y_z^3+a_2(z,y)y_z^2+a_1(z,y)y_z+a_0(z,y)=0\). We obtain a sufficient condition for the existence of a Lax representation with a certain \(L\)-matrix. We demonstrate that equations with this Lax representation possess a quadratic rational first integral. We illustrate our construction with an example of the Rayleigh-Duffing-Van der Pol oscillator with quadratic damping.Permanence of equilibrium points in the basin of attraction and existence of periodic solutions for autonomous measure differential equations and dynamic equations on time scales via generalized ODEshttps://zbmath.org/1500.340032023-01-20T17:58:23.823708Z"Federson, M."https://zbmath.org/authors/?q=ai:federson.marcia"Grau, R."https://zbmath.org/authors/?q=ai:grau.rogelio"Mesquita, J. G."https://zbmath.org/authors/?q=ai:mesquita.jaqueline-godoy"Toon, E."https://zbmath.org/authors/?q=ai:toon.eduardSummary: It is well-known that generalized ODEs encompass several types of differential equations as, for instance, functional differential equations, measure differential equations, dynamic equations on time scales, impulsive differential equations and any combinations among them, not to mention integrals equations, among others. The aim of this paper is to establish a theory of autonomous equations in the setting of generalized ODEs. Thus, we introduce the notion of autonomous generalized ODEs as well as new classes of right-hand sides for nonautonomous generalized ODEs. Amongst the main results, we prove that one of these new classes coincide with the original class of right-hand sides introduced by Kurzweil in 1957. We also prove that autonomous generalized ODEs do not enlarge the class of autonomous ODEs with uniformly continuous right-hand sides. Motivated by this fact, we then enlarge the class of autonomous generalized ODEs so that discontinuities can be taken into account. We then introduce a more general class of autonomous generalized ODEs, in whose integral form, a Stieltjes-type integral appears. A correspondence between these equations and autonomous measure differential equations is established and several results are obtained. We mention local existence and uniqueness of solutions, continuous dependence of solutions on initial values, existence of periodic solutions and permanence of asymptotically stable equilibrium point in the basin of attraction. All these results are, then, specified not only for autonomous generalized ODEs, but also for autonomous measure differential equations and dynamic equations on time scales.Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag-Leffler functionshttps://zbmath.org/1500.340042023-01-20T17:58:23.823708Z"Abbas, Mohamed I."https://zbmath.org/authors/?q=ai:abbas.mohamed-ibrahim|abbas.mohamed-i"Ragusa, Maria Alessandra"https://zbmath.org/authors/?q=ai:ragusa.maria-alessandraSummary: In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral equation in terms of Mittag-Leffler functions. The existence and uniqueness results are established by using Schauder's fixed point theorem and Banach's fixed point theorem, respectively. An example is given to illustrate the main results.Multipoint BVP for the Langevin equation under \(\varphi\)-Hilfer fractional operatorhttps://zbmath.org/1500.340052023-01-20T17:58:23.823708Z"Almalahi, Mohammed A."https://zbmath.org/authors/?q=ai:almalahi.mohammed-a"Panchal, Satish K."https://zbmath.org/authors/?q=ai:panchal.satish-kushaba"Jarad, Fahd"https://zbmath.org/authors/?q=ai:jarad.fahdSummary: In this research paper, we consider a class of boundary value problems for a nonlinear Langevin equation involving two generalized Hilfer fractional derivatives supplemented with nonlocal integral and infinite-point boundary conditions. At first, we derive the equivalent solution to the proposed problem at hand by relying on the results and properties of the generalized fractional calculus. Next, we investigate and develop sufficient conditions for the existence and uniqueness of solutions by means of semigroups of operator approach and the Krasnoselskii fixed point theorems as well as Banach contraction principle. Moreover, by means of Gronwall's inequality lemma and mathematical techniques, we analyze Ulam-Hyers and Ulam-Hyers-Rassias stability results. Eventually, we construct an illustrative example in order to show the applicability of key results.On fractional evolution inclusion coupled with a time and state dependent maximal monotone operatorhttps://zbmath.org/1500.340062023-01-20T17:58:23.823708Z"Castaing, Charles"https://zbmath.org/authors/?q=ai:castaing.charles"Godet-Thobie, C."https://zbmath.org/authors/?q=ai:godet-thobie.christiane"Saïdi, Soumia"https://zbmath.org/authors/?q=ai:saidi.soumiaSummary: The paper deals with second-order evolution problems driven by time and state dependent maximal monotone operators with non-Lipschitz perturbations. Systems governed by a couple of an evolution inclusion involving time and state dependent maximal monotone operator and a differential equation with fractional derivatives are also investigated.Existence and uniqueness of mild solutions for a fractional differential equation under Sturm-Liouville boundary conditions when the data function is of Lipschitzian typehttps://zbmath.org/1500.340072023-01-20T17:58:23.823708Z"Harjani, Jackie"https://zbmath.org/authors/?q=ai:harjani.jackie"López, Belen"https://zbmath.org/authors/?q=ai:lopez.belen"Sadarangani, Kishin"https://zbmath.org/authors/?q=ai:sadarangani.kishin-bSummary: In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its connection with a Lyapunov-type inequality.Darbo fixed point criterion on solutions of a Hadamard nonlinear variable order problem and Ulam-Hyers-Rassias stabilityhttps://zbmath.org/1500.340082023-01-20T17:58:23.823708Z"Rezapour, Shahram"https://zbmath.org/authors/?q=ai:rezapour.shahram"Bouazza, Zoubida"https://zbmath.org/authors/?q=ai:bouazza.zoubida"Souid, Mohammed Said"https://zbmath.org/authors/?q=ai:souid.mohammed-said"Etemad, Sina"https://zbmath.org/authors/?q=ai:etemad.sina"Kaabar, Mohammed K. A."https://zbmath.org/authors/?q=ai:kaabar.mohammedSummary: The existence aspects along with the stability of solutions to a Hadamard variable order fractional boundary value problem are investigated in this research study. Our results are obtained via generalized intervals and piecewise constant functions and the relevant Green function, by converting the existing Hadamard variable order fractional boundary value problem to an equivalent standard Hadamard fractional boundary problem of the fractional constant order. Further, Darbo's fixed point criterion along with Kuratowski's measure of noncompactness is used in this direction. As well as, the Ulam-Hyers-Rassias stability of the proposed Hadamard variable order fractional boundary value problem is established. A numerical example is presented to express our results' validity.\(L^1\)-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivativehttps://zbmath.org/1500.340092023-01-20T17:58:23.823708Z"Telli, Benoumran"https://zbmath.org/authors/?q=ai:telli.benoumran"Souid, Mohammed Said"https://zbmath.org/authors/?q=ai:souid.mohammed-saidSummary: In this paper, we study the existence of integrable solutions for initial value problems for fractional order implicit differential equations with Hadamard fractional derivative. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem.Existence and uniqueness of solutions to anti-periodic Riezs-Caputo impulsive fractional boundary value problemshttps://zbmath.org/1500.340102023-01-20T17:58:23.823708Z"Toprakseven, Suayip"https://zbmath.org/authors/?q=ai:toprakseven.suayipSummary: In this paper, we prove the existence and uniqueness of solutions for a class of impulsive fractional initial/boundary value problems of the Riesz-Caputo differential equation with anti-peroidic boundary condition. In the final section, we give some numerical examples to verify the theoretical results.On the solvability of a nonlinear Langevin equation involving two fractional orders in different intervalshttps://zbmath.org/1500.340112023-01-20T17:58:23.823708Z"Turab, Ali"https://zbmath.org/authors/?q=ai:turab.ali"Sintunavarat, Wutiphol"https://zbmath.org/authors/?q=ai:sintunavarat.wutipholSummary: This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.Parameter estimation of fractional uncertain differential equations via Adams methodhttps://zbmath.org/1500.340122023-01-20T17:58:23.823708Z"Wu, Guo-Cheng"https://zbmath.org/authors/?q=ai:wu.guocheng"Wei, Jia-Li"https://zbmath.org/authors/?q=ai:wei.jia-li"Luo, Cheng"https://zbmath.org/authors/?q=ai:luo.cheng"Huang, Lan-Lan"https://zbmath.org/authors/?q=ai:huang.lanlanSummary: Parameter estimation of uncertain differential equations becomes popular very recently. This paper suggests a new method based on fractional uncertain differential equations for the first time, which hold more parameter freedom degrees. The Adams numerical method and Adam algorithm are adopted for the optimization problems. The estimation results are compared to show a better forecast. Finally, the predictor-corrector method is adopted to solve the fractional uncertain differential equations. Numerical solutions are demonstrated with varied \(\alpha\)-paths.Symmetric ground state solutions for the Choquard Logarithmic equation with exponential growthhttps://zbmath.org/1500.340132023-01-20T17:58:23.823708Z"Yuan, Shuai"https://zbmath.org/authors/?q=ai:yuan.shuai"Chen, Sitong"https://zbmath.org/authors/?q=ai:chen.sitongSummary: We investigate the existence of ground state solutions for the fractional Choquard Logarithmic equation
\[
(- \Delta)^{1 / 2} u + V (x) u + (\ln | \cdot | \ast | u |^2) u = f (u), \quad x \in \mathbb{R},
\]
where \(V \in \mathcal{C} (\mathbb{R}, [ 0, \infty))\) and the \(f\) satisfies exponential critical growth. The present paper extends and complements the result of \textit{E. S. Böer} and \textit{O. H. Miyagaki} [``The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth'', Preprint, \url{arXiv:2011.12806}]. In particular, our paper has two typical features. Firstly, using a weaker assumption on \(f\), we establish the energy inequality to exclude the vanishing case of the required Cerami sequence. Secondly, with the property of radial symmetry we shall use some new variational and analytic technique to establish our final result which is different to the arguments explored in [loc. cit.].The uniqueness and iterative properties of solutions for a general Hadamard-type singular fractional turbulent flow modelhttps://zbmath.org/1500.340142023-01-20T17:58:23.823708Z"Zhang, Xinguang"https://zbmath.org/authors/?q=ai:zhang.xinguang"Xu, Pengtao"https://zbmath.org/authors/?q=ai:xu.pengtao"Wu, Yonghong"https://zbmath.org/authors/?q=ai:wu.yonghong.1"Wiwatanapataphee, Benchawan"https://zbmath.org/authors/?q=ai:wiwatanapataphee.benchawanIn this paper, the iterative properties of positive solutions for a general Hadamard-type singular fractional turbulent flow model involving a nonlinear operator are obtained. The uniqueness of positive solutions for the corresponding model are given based on a double monotone iterative technique and the properties of the Green function. Furthermore, the iterative analysis for the unique solution are established including the iterative schemes converging to the unique solution, error estimates, convergence rate and entire asymptotic behavior. This paper is a supplement to the existing related Hadamard fractional-order differential equation boundary value problems.
Reviewer: Wengui Yang (Sanmenxia)A logic based approach to finding real singularities of implicit ordinary differential equationshttps://zbmath.org/1500.340152023-01-20T17:58:23.823708Z"Seiler, Werner M."https://zbmath.org/authors/?q=ai:seiler.werner-m"Seiß, Matthias"https://zbmath.org/authors/?q=ai:seiss.matthias"Sturm, Thomas"https://zbmath.org/authors/?q=ai:sturm.thomasSummary: We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be characterised as points where the behaviour of a certain linear system of equations changes. These points can be discovered using a specifically adapted parametric generalisation of Gaussian elimination combined with heuristic simplification techniques and real quantifier elimination methods. We demonstrate the relevance and applicability of our approach with computational experiments using a prototypical implementation in \textsc{Reduce}.Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz systemhttps://zbmath.org/1500.340162023-01-20T17:58:23.823708Z"Algaba, A."https://zbmath.org/authors/?q=ai:algaba.antonio"Domínguez-Moreno, M. C."https://zbmath.org/authors/?q=ai:dominguez-moreno.maria-c"Merino, M."https://zbmath.org/authors/?q=ai:merino.manuel"Rodríguez-Luis, A. J."https://zbmath.org/authors/?q=ai:rodriguez-luis.alejandro-jAuthors' abstract: In this paper we consider a 3D three-parameter unfolding close to the normal form of the triple-zero bifurcation exhibited by the Lorenz system. First we study analytically the double-zero degeneracy (a double-zero eigenvalue with geometric multiplicity two) and two Hopf bifurcations. We focus on the more complex case in which the double-zero degeneracy organizes several codimension-one singularities, namely transcritical, pitchfork, Hopf and heteroclinic bifurcations. The analysis of the normal form of a Hopf-transcritical bifurcation allows to obtain the expressions for the corresponding bifurcation curves. A degenerate double-zero bifurcation is also considered. The theoretical information obtained is very helpful to start a numerical study of the 3D system. Thus, the presence of degenerate heteroclinic and homoclinic orbits, T-point heteroclinic loops and chaotic attractors is detected. We find numerical evidence that, at least, four curves of codimension-two global bifurcations are related to the triple-zero degeneracy in the system analyzed.
Reviewer: Yong Ye (Shenzhen)On the isochronous center of planar piecewise polynomial potential systemshttps://zbmath.org/1500.340172023-01-20T17:58:23.823708Z"Liu, Changjian"https://zbmath.org/authors/?q=ai:liu.changjian"Wang, Shaoqing"https://zbmath.org/authors/?q=ai:wang.shaoqingSummary: This paper is devoted to the isochronicity of two kinds of planar piecewise polynomial potential systems separated by \(x\)-axis and \(y\)-axis, respectively. By means of the expansion of the period function near the infinity, we obtain in this paper that for these two cases, the piecewise potential system has an isochronous center at the origin if and only if the subsystems are linear. It is however not true in the analytic scenario; one can find in the paper by \textit{F. Mañosas} and \textit{P. J. Torres} [Proc. Am. Math. Soc. 133, No. 10, 3027--3035 (2005; Zbl 1079.34018)] that the isochronicity of the center of the piecewise analytic potential system cannot imply the linearity of the two subsystems.The cyclicity of a class of global nilpotent center under perturbations of piecewise smooth polynomials with four zoneshttps://zbmath.org/1500.340182023-01-20T17:58:23.823708Z"Zou, Li"https://zbmath.org/authors/?q=ai:zou.li"Zhao, Liqin"https://zbmath.org/authors/?q=ai:zhao.liqinSummary: In this paper, we study the bifurcation of limit cycles of near-Hamilton system with four zones separated by nonlinear switching curves. We derive the expression of the first order Melnikov function. As an application, we consider the cyclicity of the system \(\dot{x}=y\), \(\dot{y}=-x^{2m-1}\), where \((0, 0)\) is a global nilpotent center and \(2\le m\in\mathbb{N}^+\), under the perturbations of piecewise smooth polynomials with four zones separated by \(y=\pm kx^m\) with \(k>0\). By analyzing the first order Melnikov function, we obtain the exact bound of the number of limit cycles bifurcating from the period annulus if the first order Melnikov function is not identically zero. We also give some examples to illustrate our results.Isolating neighborhoods and their stability for differential inclusions and Filippov systemshttps://zbmath.org/1500.340192023-01-20T17:58:23.823708Z"Thieme, Cameron"https://zbmath.org/authors/?q=ai:thieme.cameronSummary: Conley index theory is a powerful topological tool for obtaining information about invariant sets in dynamical systems. A key feature of Conley theory is that the index is robust under perturbation; given a continuous family of flows \(\{\varphi_{\lambda}\}\), the index remains constant over a range of parameter values, avoiding many of the complications associated with bifurcations. This theory is well-developed for flows and homeomorphisms, and has even been extended to certain classes of semiflows. However, in recent years mathematicians and scientists have become interested in differential inclusions. Here the theory has also been studied for inclusions which satisfy certain bounding properties. In this paper we extend some of these results-in particular, the stability of isolating neighbourhoods under perturbation-to inclusions which do not satisfy these bounding properties. We do so by utilizing a novel approach to the solution set of differential inclusions which results in an object called a multiflow. This perspective allows us to relax the assumptions of the earlier work and also to develop tools needed to extend the continuation of Conley's attractor-repeller decomposition to differential inclusions, a result which is addressed in subsequent work. Our interest in these results is in the study of piecewise-continuous differential equations-which are typically reframed as a certain type of differential inclusion called Filippov systems-and how these discontinuous equations relate to families of smooth systems which limit to them. Therefore this paper also discusses in some detail how the generalization of Conley index theory applies to Filippov systems.Spectral properties of a beam equation with eigenvalue parameter occurring linearly in the boundary conditionshttps://zbmath.org/1500.340202023-01-20T17:58:23.823708Z"Aliyev, Ziyatkhan S."https://zbmath.org/authors/?q=ai:aliyev.ziyatkhan-s"Mamedova, Gunay T."https://zbmath.org/authors/?q=ai:mamedova.gunay-tThe paper is concerned with the eigenvalue problem
\[
\begin{cases} l(y)(x)\equiv y^{(4)}(x)-(q(x)y'(x))'=\lambda y(x), \quad 0<x<1,\\
y''(0)=0,\\
Ty(0)-a\lambda y(0)=0,\\
y'(1)\cos \gamma+y''(1)\sin \gamma=0,\\
Ty(1)-c\lambda y(1)=0, \end{cases}\tag{1}
\]
where \(\lambda\in \mathbb{C}\) is a spectral parameter, the operator \(T\) is defined by \(Ty=y'''-q y'\), the function \(q\) is absolutely continuous and positive on \([0,1]\), \(a,\,c\) and \(\gamma\) are real constants with \(a<0\), \(c<0\) and \(\gamma\in [0,\pi/2]\). The authors investigate the position of the eigenvalues on the real axis, the structure of root subspaces, and the oscillatory properties of the eigenfunctions which correspond to both positive and negative eigenvalues of problem \((1)\). Then they obtain asymptotic formulas for the eigenvalues and eigenfunctions of \((1)\). Sufficient conditions for the subsystems of root functions to form a basis in the space \(L_p\), \(1<p<\infty\) are finally presented.
Reviewer: Rodica Luca (Iaşi)A family of two-point boundary value problems for loaded differential equationshttps://zbmath.org/1500.340212023-01-20T17:58:23.823708Z"Assanova, A. T."https://zbmath.org/authors/?q=ai:assanova.anar-turmaganbetkyzy"Zholamankyzy, A."https://zbmath.org/authors/?q=ai:zholamankyzy.ainurAuthors' abstract: A family of two-point boundary value problems for loaded differential equations is considered on a rectangular domain. By introducing new additional functions, the considered problem is reduced to an equivalent family of problems for differential equations with parameters. Sufficient existence conditions for a unique solution to the family of two-point boundary value problems for loaded differential equations are established in terms of input data.
Reviewer: Haiyan Wang (Phoenix)Green's functions, linear second-order differential equations, and one-dimensional diffusion advection modelshttps://zbmath.org/1500.340222023-01-20T17:58:23.823708Z"Yu, Xiao"https://zbmath.org/authors/?q=ai:yu.xiao"Lan, Kunquan"https://zbmath.org/authors/?q=ai:lan.kunquan"Wu, Jianhong"https://zbmath.org/authors/?q=ai:wu.jianhongIn the article, Green's functions to linear second-order ordinary differential equations with general separated boundary conditions are derived for any parameters. The previously unknown properties of the Green function with possibly negative parameters are obtained. The results obtained in the article are used to derive and study the Green's function arising from steady-state solutions of a one-dimensional diffusion-advection model used in chemical reactor theory and mathematical biology.
Reviewer: Tatuana Badokina (Saransk)Infinitesimal center problem on zero cycles and the composition conjecturehttps://zbmath.org/1500.340232023-01-20T17:58:23.823708Z"Álvarez, A."https://zbmath.org/authors/?q=ai:alvarez.amelia"Bravo, J. L."https://zbmath.org/authors/?q=ai:bravo.jose-luis"Christopher, C."https://zbmath.org/authors/?q=ai:christopher.colin-j"Mardešić, P."https://zbmath.org/authors/?q=ai:mardesic.pavaoIn this paper, the authors study the zero-dimensional version of the infinitesimal center problem, which is the analog of the classical infinitesimal center problem in the plane, but for zero cycles. They define the displacement function and prove that it is identically zero if and only if the deformation has a composition factor. That is, they prove that the composition conjecture is true for the infinitesimal center problem on zero cycles, though it is not true for the tangential center problem. Finally, some examples of applications of the main results are given. Note that the authors consider only the polynomial case, but the problems and some of the results can be extended to a more general setting.
Reviewer: Xiuli Cen (Zhuhai)Isochronous and strongly isochronous foci of polynomial Liénard systemshttps://zbmath.org/1500.340242023-01-20T17:58:23.823708Z"Amel'kin, V. V."https://zbmath.org/authors/?q=ai:amelkin.vladimir-vasilievichA two-dimensional Liénard system having an isochronous focus at the origin is studied. A normal form is proposed to this end to study the global behavior of the system.
Reviewer: Gheorghe Tigan (Timișoara)On the limit cycles for a class of generalized Liénard differential systemshttps://zbmath.org/1500.340252023-01-20T17:58:23.823708Z"Diab, Zouhair"https://zbmath.org/authors/?q=ai:diab.zouhair"Guirao, Juan L. G."https://zbmath.org/authors/?q=ai:garcia-guirao.juan-luis"Vera, Juan A."https://zbmath.org/authors/?q=ai:vera.juan-aThe existence of limit cycles of a class of piecewise two-dimensional generalized Liénard systems is studied by the method of averaging theory. It is proven that the maximum number of limit cycles is $[n/2]+1$.
Reviewer: Gheorghe Tigan (Timișoara)Large speed traveling waves for the Rosenzweig-MacArthur predator-prey model with spatial diffusionhttps://zbmath.org/1500.340262023-01-20T17:58:23.823708Z"Ducrot, Arnaud"https://zbmath.org/authors/?q=ai:ducrot.arnaud"Liu, Zhihua"https://zbmath.org/authors/?q=ai:liu.zhihua"Magal, Pierre"https://zbmath.org/authors/?q=ai:magal.pierreAuthors' abstract: This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur predator-prey model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic wave train solution in the large wave speed asymptotic. Depending on the model parameters we more particularly study the existence and uniqueness of a traveling wave connecting two equilibria or connecting an equilibrium point and a periodic wave train. We also discuss the existence and uniqueness of such a periodic wave train. Our analysis is based on ordinary differential equation techniques by coupling the theories of invariant manifolds together with those of global attractors.
Reviewer: Minh Van Nguyen (Little Rock)The center problem for the class of \(\varLambda-\varOmega\) differential systemshttps://zbmath.org/1500.340272023-01-20T17:58:23.823708Z"Llibre, Jaume"https://zbmath.org/authors/?q=ai:llibre.jaume"Ramírez, Rafael"https://zbmath.org/authors/?q=ai:ramirez.rafael-o"Ramírez, Valentín"https://zbmath.org/authors/?q=ai:ramirez.valentinThe article deals with planar analytical and polynomial differential systems having a weak center at the origin. The center is called weak if the first Poincaré-Lyapunov integral of the system can be written as \(H=1/2\left(x^{2} +y^{2} \right)\left(1+\mathrm{h.o.t.}\right)\). In [\textit{M. A. M. Alwash} and \textit{N. G. Lloyd}, Proc. R. Soc. Edinb., Sect. A, Math. 105, 129--152 (1987; Zbl 0618.34026)] sufficient conditions are given for the existence of the center of plane systems whose nonlinear parts are homogeneous polynomials of the same degree. The article assumes the fulfillment of similar conditions for arbitrary nonlinearities (polynomial or holomorphic) and raises the question of the presence of a weak center at the origin. The theorem on necessary and sufficient conditions of a weak center is proved when these conditions are met. In addition, it is proved that any analytic (polynomial) vector field with a weak center at zero is quasi-Darboux integrable. There are inaccuracies in the article: theorem 2, proved, according to the authors, in [\textit{J. Llibre} et al., Rend. Circ. Mat. Palermo (2) 68, No. 1, 29--64 (2019; Zbl 1423.34032)] is not true and is not contained in this work. Any planar system of the class under consideration (and not only with a weak center) can be written in the form as it is formulated in Theorem 2.
Reviewer: Alexander Rudenok (Minsk)Non-existence and uniqueness of limit cycles in a class of generalized Liénard equationshttps://zbmath.org/1500.340282023-01-20T17:58:23.823708Z"Llibre, Jaume"https://zbmath.org/authors/?q=ai:llibre.jaume"Valls, Claudia"https://zbmath.org/authors/?q=ai:valls.claudiaGeneralized Liénard systems of the form
\[
\dot{x} = y+ax^p+by^k, \dot{y} = cx^m,\hspace{9cm} (1)
\]
where \(n, k, m\) are positive integers, \(1<n<k,\) and \(a, b, c\in\mathbb{R}\) with \(bc\neq0\) are considered. It is proved that:
1) with a change of variables and a rescaling of the time, system (1) is equivalent to the following two systems
\[
\dot{x} = y+ax^p+by^k, \dot{y} = x^m,\hspace{9cm} (i)
\]
\[
\dot{x} = y+ax^p+by^k, \dot{y} = -x^m,\hspace{8.5cm} (ii)
\]
2) for \(m\) even, neither systems (i) nor systems (ii) have limit cycles,
3) for \(m\) odd, systems (i) do not have limit cycles,
4) for \(m,\) odd systems (ii) have limit cycles if and only if \(k\) and \(n\) are odd and \(a<0.\) In this case, the maximum number of limit cycles that system (ii) can have is one and this upper bound is reached. Moreover, whenever the limit cycle exists, it is hyperbolic.
Reviewer: Valentine Tyshchenko (Grodno)The period function of quadratic generalized Lotka-Volterra systems without complex invariant lineshttps://zbmath.org/1500.340292023-01-20T17:58:23.823708Z"Long, Teng"https://zbmath.org/authors/?q=ai:long.teng"Liu, Changjian"https://zbmath.org/authors/?q=ai:liu.changjian"Wang, Shaoqing"https://zbmath.org/authors/?q=ai:wang.shaoqingThe authors analyze the monotonicity of period function of the planar generalized quadratic Lotka-Volterra systems. By taking two invariant lines as new coordinate axes and making a constant time scale change to transform the systems and simplify the first integrals, it is proved for the case without complex invariant lines that the period function is monotone increasing.
Reviewer: Fengqin Zhang (Yuncheng)The least possible impulse for oscillating all nontrivial solutions of second-order nonoscillatory differential equationshttps://zbmath.org/1500.340302023-01-20T17:58:23.823708Z"Sugie, Jitsuro"https://zbmath.org/authors/?q=ai:sugie.jitsuroThe author considers the impulsive differential equation
\[
\begin{aligned}
&x''+c(t)\,x=0\,,\quad t\neq \theta_k>t_0\;\\
& \Delta x'(\theta_k)+b_k\,x(\theta_k)=0\,,
\end{aligned}
\]
where \(c\) is a continuous real-valued function on \([t_0,\infty]\), \(\{ \theta_k\}\) is a sequence satisfying \(\theta_i<\theta_{i+1}\) for \(i\in\mathbb{N}\) and \(\lim_{k\to\infty}\theta_k=\infty\), \(\Delta\) is the difference operator \(\Delta z(\theta_k)=z(\theta_k^+)-z(\theta_k^-)\), and \(\{b_k\}\) is a sequence of positive real numbers.\par The aim of the paper is to calculate the least amount of impulse required to change the nonoscillatory character of the solutions of the second order linear differential equation \(x''+c(t)\,x=0\,\) to oscillatory.
Reviewer: Sylvia Novo (Valladolid)Bifurcations from families of periodic solutions in piecewise differential systemshttps://zbmath.org/1500.340312023-01-20T17:58:23.823708Z"Llibre, Jaume"https://zbmath.org/authors/?q=ai:llibre.jaume"Novaes, Douglas D."https://zbmath.org/authors/?q=ai:novaes.douglas-duarte"Rodrigues, Camila A. B."https://zbmath.org/authors/?q=ai:rodrigues.camila-ap-bSummary: Consider a differential system of the form
\[
x^\prime = F_0(t, x) + \sum_{i = 1}^k \varepsilon^i F_i (t, x) + \varepsilon^{k + 1} R(t, x, \varepsilon),
\]
where \(F_i : \mathbb{S}^1 \times D \to \mathbb{R}^m\) and \(R : \mathbb{S}^1 \times D \times (-\varepsilon_0, \varepsilon_0) \to \mathbb{R}^m\) are piecewise \(C^{k + 1}\) functions and \(T\)-periodic in the variable \(t\). Assuming that the unperturbed system \(x^\prime = F_0(t, x)\) has a \(d\)-dimensional submanifold of periodic solutions with \(d < m\), we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated \(T\)-periodic solutions of the above differential system.Admissible perturbations of a generalized langford systemhttps://zbmath.org/1500.340322023-01-20T17:58:23.823708Z"Musafirov, Eduard"https://zbmath.org/authors/?q=ai:musafirov.eduard-v"Grin, Alexander"https://zbmath.org/authors/?q=ai:grin.alexander-a"Pranevich, Andrei"https://zbmath.org/authors/?q=ai:pranevich.andrei-fIn this paper, the authors construct admissible perturbations for the generalized Langford system, which have the same Mironenko reflecting function, and prove the instability of the equilibrium point of the admissibly perturbed systems, also present the conditions under which admissibly perturbed systems have periodic solutions, as well as conditions for the asymptotic stability (instability) of the periodic solutions. Finally, using numerical simulations, similar chaotic attractors of the generalized Langford system and an admissibly perturbed system are shown.
Reviewer: Xiong Li (Beijing)On the stability of integral manifolds of a system of ordinary differential equations in the critical casehttps://zbmath.org/1500.340332023-01-20T17:58:23.823708Z"Kuptsov, M. I."https://zbmath.org/authors/?q=ai:kuptsov.michail-i"Minaev, V. A."https://zbmath.org/authors/?q=ai:minaev.v-a.1"Faddeev, A. O."https://zbmath.org/authors/?q=ai:faddeev.a-o"Yablochnikov, S. L."https://zbmath.org/authors/?q=ai:yablochnikov.s-lSummary: In this paper, we consider the stability problem for nonzero integral manifolds of a nonlinear, finite-dimensional system of ordinary differential equations whose right-hand side is a vector-valued function containing a parameter and periodic in an independent variable. We assume that the system possesses a trivial integral manifold for all values of the parameter and the corresponding linear subsystem does not possess the exponential dichotomy property.We find sufficient conditions for the existence of a nonzero integral manifold in a neighborhood of the equilibrium of the system and conditions for its stability or instability. For this purpose, based of the ideas of the Lyapunov method and the method of transform matrices, we construct operators that allow one to reduce the solution of this problem to the search for fixed points.Resonance oscillation and transition to chaos in \(\phi^8\)-Duffing-van der Pol oscillatorhttps://zbmath.org/1500.340342023-01-20T17:58:23.823708Z"Adelakun, A. O."https://zbmath.org/authors/?q=ai:adelakun.a-oFollowing the study of a Duffing-Van der Pol oscillator of which the potential function is a polynomial of degree six, the author extend his investigation of the oscillator to the potential function of degree eight. It seems that the new system exhibits much richer nonlinear behavior than the previous one. From numerical simulations, even though the system with degree six is stable, a small value of the coefficient of the degree-eight term already induces very complex dynamical behavior such as the coexistence of multiple limit cycles, period-doubling route to chaos and sudden chaos. An electronic circuit was also designed to confirm to a great extent the theoretical and simulation results.
Reviewer: Kwok-wai Chung (Hong Kong)Stage-structured models for interactive wild and periodically and impulsively released sterile mosquitoeshttps://zbmath.org/1500.340352023-01-20T17:58:23.823708Z"Ai, Shangbing"https://zbmath.org/authors/?q=ai:ai.shangbing"Li, Jia"https://zbmath.org/authors/?q=ai:li.jia"Yu, Jianshe"https://zbmath.org/authors/?q=ai:yu.jian-she"Zheng, Bo"https://zbmath.org/authors/?q=ai:zheng.bo.1Summary: A two-dimensional stage-structured model for the interactive wild and sterile mosquitoes is derived where the wild mosquito population is composed of larvae and adult classes and only sexually active sterile mosquitoes are included as a function given in advance. The strategy of constant releases of sterile mosquitoes is considered but periodic and impulsive releases are more focused on. Local stability of the origin and the existence of a positive periodic solution are investigated. While mathematical analysis is more challenging, numerical examples demonstrate that the model dynamics, determined by thresholds of the release amount and the release waiting period, essentially match the dynamics of the alike one-dimensional models. It is also shown that richer dynamics are exhibited from the two-dimensional stage-structured model.Analysis of dengue fever outbreak by generalized fractional derivativehttps://zbmath.org/1500.340362023-01-20T17:58:23.823708Z"Bosch, Paul"https://zbmath.org/authors/?q=ai:bosch.paul-j"Gómez-Aguilar, J. F."https://zbmath.org/authors/?q=ai:gomez-aguilar.jose-francisco"Rodríguez, José M."https://zbmath.org/authors/?q=ai:rodriguez.jose-manuel"Sigarreta, José M."https://zbmath.org/authors/?q=ai:sigarreta-almira.jose-mariaFractional calculus is successfully used to model a broad range of problems, since the evolution of many physical processes can be more precisely described with fractional derivatives. The authors study some general properties of fractional Gaussian model with the conformable fractional derivative. In particular, they use a generalized conformable fractional derivative in order to study a Gaussian model. Taking into account an experimental dataset, they solve an inverse problem to estimate the order of the involved fractional derivative. From the above results, it is inferred that the conformable approach minimizes the error in the adjustments in relation to the other models studied.
Reviewer: Ismail Huseynov (Mersin)A dynamic \textit{\(SI_q\) IRV} mathematical model with non-linear force of isolation, infection and curehttps://zbmath.org/1500.340372023-01-20T17:58:23.823708Z"Chatzarakis, G. E."https://zbmath.org/authors/?q=ai:chatzarakis.george-e"Dickson, S."https://zbmath.org/authors/?q=ai:dickson.stewart"Padmasekaran, S."https://zbmath.org/authors/?q=ai:padmasekaran.sSummary: The Susceptible-Isolated-Infected-Recovered-Vaccinated (\textit{\(SI_q\)IRV}) deterministic model is examined in this paper. This model considers a nonlinear force of quarantine, infection and care, where vaccinated individuals lose their immunity after a period of time and become susceptible to infection. Isolation is the main key to bringforth the S\textit{\(I_q\)}IRV model. The fundamentals of reproduction number calculated using this model is an outbreak threshold that decides whether or not a disease can spread. The infection free steady state solutions are locally and globally found to be asymptotically stable when \(R_0 < 1\). Infection persistent steady state solutions are also found to be locally asymptotically stable when \(R_0 > 1\). At the end, computational simulations were run to confirm and support our theoretical findings.Differential equationshttps://zbmath.org/1500.340382023-01-20T17:58:23.823708Z"Fatheddin, Parisa"https://zbmath.org/authors/?q=ai:fatheddin.parisaSummary: We offer an exposition of various differential equation models used in the literature to investigate the spread of computer viruses and cyber-attacks. The goal is to bring to light and explain some recent research developments regarding cybersecurity. There are two main ideas in modeling problems by differential equations in this field. One is to use models in epidemiology such as the Susceptible-Infected-Recovered model, to view a computer virus as a disease spreading in a network of computers, and the goal is to determine the basic reproductive number, for which the global stability is found based on techniques offered in a regular undergraduate textbook. The second type of model in cybersecurity is cyber-attacks, which are mainly categorized as deception or denial of service attacks. Deception attacks manipulate the data and deceive the receiver; whereas, the denial of service attack jams or delays the connection preventing the receiver from obtaining the information. The stability and when an attack is undetectable or unidentifiable are discussed, and their proofs are explained. The concepts, methods, and reasoning in the proofs in this chapter are made to align with those covered in typical undergraduate-level courses in differential equations and linear algebra.
For the entire collection see [Zbl 1484.05004].Qualitative analysis of an HIV/AIDS model with treatment and nonlinear perturbationhttps://zbmath.org/1500.340392023-01-20T17:58:23.823708Z"Gao, Miaomiao"https://zbmath.org/authors/?q=ai:gao.miaomiao"Jiang, Daqing"https://zbmath.org/authors/?q=ai:jiang.daqing"Hayat, Tasawar"https://zbmath.org/authors/?q=ai:hayat.tasawarSummary: In this paper, we consider a high-dimensional stochastic HIV/AIDS model that incorporates both multiple stages treatment and higher order perturbation. Firstly, we establish sufficient criteria for the existence of a unique ergodic stationary distribution by making use of stochastic Lyapunov analysis method. Stationary distribution shows that the disease will be persistent in the long term. Then, conditions for extinction of the disease are obtained. Theoretical analysis indicates that large noise intensity can suppress the prevalence of HIV/AIDS epidemic. Finally, we provide some numerical simulations to illustrate the analytical results.Dynamics of a stochastic HIV/AIDS model with treatment under regime switchinghttps://zbmath.org/1500.340402023-01-20T17:58:23.823708Z"Gao, Miaomiao"https://zbmath.org/authors/?q=ai:gao.miaomiao"Jiang, Daqing"https://zbmath.org/authors/?q=ai:jiang.daqing"Hayat, Tasawar"https://zbmath.org/authors/?q=ai:hayat.tasawar"Alsaedi, Ahmed"https://zbmath.org/authors/?q=ai:alsaedi.ahmed"Ahmad, Bashir"https://zbmath.org/authors/?q=ai:ahmad.bashir.1|ahmad.bashir.2Summary: This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.Hidden synchronization in phase locked loop systemshttps://zbmath.org/1500.340412023-01-20T17:58:23.823708Z"Mamonov, S. S."https://zbmath.org/authors/?q=ai:mamonov.sergei-stanislavovich"Ionova, I. V."https://zbmath.org/authors/?q=ai:ionova.irina-viktorovna"Kharlamova, A. O."https://zbmath.org/authors/?q=ai:kharlamova.anastasiya-olegovnaSummary: This paper is devoted to the analysis of frequency-phase locked loop systems (FPLL). The mathematical model of such systems is a system of differential equations with a cylindrical phase space. For FPLL systems, we obtain conditions of latent synchronization.New fractional modelling, analysis and control of the three coupled multiscale non-linear buffering systemhttps://zbmath.org/1500.340422023-01-20T17:58:23.823708Z"Partohaghighi, Mohammad"https://zbmath.org/authors/?q=ai:partohaghighi.mohammad"Yusuf, Abdullahi"https://zbmath.org/authors/?q=ai:yusuf.abdullahi-a"Bayram, Mustafa"https://zbmath.org/authors/?q=ai:bayram.mustafaSummary: This study aims to investigate the complicated dynamical \(HCO_3^-/CO_2\) buffering system using fractional operators which is not been investigated yet. We consider a new fractional mathematical model in the frame of fractional-order differential equations. In the proposed fractional-order model, we apply the Caputo-Fabrizio fractional operator with an exponential kernel. Then to solve the derived system of fractional equations, we suggest a quadratic numerical technique and prove its stability and convergence. Also, accurate control for the proposed system is considered. Behaviors of the approximate solutions for the considered model are provided by choosing different values of fractional orders along with integer order. Each figure manifests and compares the numerical solutions under selected orders. Figures, show how the results can be affected by changing the fractional orders.Phase diffusion and noise temperature of a microwave amplifier based on single unshunted Josephson junctionhttps://zbmath.org/1500.340432023-01-20T17:58:23.823708Z"Ryabov, Artem"https://zbmath.org/authors/?q=ai:ryabov.artem"Žonda, Martin"https://zbmath.org/authors/?q=ai:zonda.martin"Novotný, Tomáš"https://zbmath.org/authors/?q=ai:novotny.tomasSummary: High-gain microwave amplifiers operating near quantum limit are crucial for development of quantum technology. However, a systematic theoretical modeling and simulations of their performance represent rather challenging tasks due to the occurrence of colored noises and nonlinearities in the underlying circuits. Here, we develop a response theory for such an amplifier whose circuit dynamics is based on nonlinear oscillations of an unshunted Josephson junction. The theory accounts for a subtle interplay between exponentially damped fluctuations around the stable limit cycle and the nonlinear dynamics of the limit cycle phase. The amplifier gain and noise spectrum are derived assuming a colored voltage noise at the circuit resistor. The derived expressions are generally applicable to any system whose limit cycle dynamics is perturbed by a colored noise and a harmonic signal. We also critically assess reliabilities of numerical methods of simulations of the corresponding nonlinear Langevin equations, where even reliable discretization schemes might introduce errors significantly affecting simulated characteristics at the peak performance.Synchronization and self-organization in complex networks for a tuberculosis modelhttps://zbmath.org/1500.340442023-01-20T17:58:23.823708Z"Silva, Cristiana J."https://zbmath.org/authors/?q=ai:silva.cristiana-j"Cantin, Guillaume"https://zbmath.org/authors/?q=ai:cantin.guillaumeSummary: In this work, we propose and analyze the dynamics of a complex network built with non identical instances of a tuberculosis (TB) epidemiological model, for which we prove the existence of non-negative and bounded global solutions. A two nodes network is analyzed where the nodes represent the TB epidemiological situation of the countries Angola and Portugal. We analyze the effect of different coupling and intensity of migratory movements between the two countries and explore the effect of seasonal migrations. For a random complex network setting, we show that it is possible to reach a synchronization state by increasing the coupling strength and test the influence of the topology in the dynamics of the complex network. All the results are analyzed through numerical simulations where the given algorithms are implemented with the python 3.5 language, in a Debian/GNU-Linux environment.Influence of Allee effect in prey and hunting cooperation in predator with Holling type-III functional responsehttps://zbmath.org/1500.340452023-01-20T17:58:23.823708Z"Vishwakarma, Krishnanand"https://zbmath.org/authors/?q=ai:vishwakarma.krishnanand"Sen, Moitri"https://zbmath.org/authors/?q=ai:sen.moitriSummary: Cooperative hunting is a widespread phenomenon in the predator population which promotes the predation and the coexistence of the prey-predator system. On the other hand, the Allee effect among prey may drive the system to instability. In this work, we consider a prey-predator model with Type-III functional response involving the hunting cooperation in predator and Allee effect in the growth rate of the prey population. Here our aim mainly is to demonstrate the impact of both the Allee effect and hunting cooperation on the system dynamics. Mathematically our analysis primarily focuses on the stability of coexisting equilibrium points and all possible bifurcations that the system may exhibit. We have observed transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and SN-TC bifurcation point respectively in the course of studying the global dynamics.Exact synchronization and asymptotic synchronization for linear ODEshttps://zbmath.org/1500.340462023-01-20T17:58:23.823708Z"Wang, Lijuan"https://zbmath.org/authors/?q=ai:wang.lijuan"Yan, Qishu"https://zbmath.org/authors/?q=ai:yan.qishuAuthors' abstract: This paper studies exact synchronization and asymptotic synchronization problems for a controlled linear system of ordinary differential equations. In this paper, we build up necessary and sufficient conditions for exact synchronization and asymptotic synchronization problems. When a system is not controllable but exactly synchronizable, it can be asymptotically synchronized in any given rate and the state of exact synchronization is given. However, when a system is not controllable and can be asymptotically synchronized in any given rate, it may not be exactly synchronizable.
Reviewer: Jiu-Gang Dong (Dalian)Stability and asymptotic stability in terms of two measures with initial time differencehttps://zbmath.org/1500.340472023-01-20T17:58:23.823708Z"Yakar, Coşkun"https://zbmath.org/authors/?q=ai:yakar.coskun"Mohammed, Sami"https://zbmath.org/authors/?q=ai:mohammed.samiSummary: We have investigated the stability criteria of dynamic system by using several Lyapunov functions with initial time difference and applied the several Lyapunov functions to a obtain stability and asymptotic stability in terms of two measures by using two or more Lyapunov-like functions with initial time difference.On the stability of the zero solution of a differential equation of the second order in a critical casehttps://zbmath.org/1500.340482023-01-20T17:58:23.823708Z"Dorodenkov, A. A."https://zbmath.org/authors/?q=ai:dorodenkov.a-aAuthor's abstract: Differential equations of the form \(\ddot{x}+x^{2}~\mathrm{sgn}~ x=Y(t,x,\dot{x})\) are considered, in which the right-hand side is a small periodic perturbation of \(t\), a sufficiently differentiable function in the origin neighborhood with variables \( x, \dot{x}\) [\textit{Yu. N. Bibikov}, Math. Notes 65, No. 3, 269--279 (1999; Zbl 0962.37024); translation from Mat. Zametki 65, No. 3, 323--335 (1999)]. It is assumed that \(X\) perturbation is of an order of smallness not lower than the fifth if \( x \) is assigned the second order and \(\dot{x} \) is assigned the third order. Periodic functions are introduced that are solutions of the equation above with a zero right-hand side. Since the differentiability of the quadratic part is bounded, the differentiability of the introduced functions is also bounded. These functions are used to switch from the initial equation to a system of equations in coordinates similar to polar. This system, with the help of polynomial replacement, is reduced to a system with Lyapunov constants. Replacement coefficients are found by partial fraction decomposition. A conclusion regarding the nature of the stability of the zero solution is drawn on the basis of the sign of the first nonzero constant [\textit{A. A. Dorodenkov}, Vestn. St. Petersbg. Univ., Math. 42, No. 4, 262--268 (2009; Zbl 1194.34070); translation from Vestn. St-Peterbg. Univ.,Ser. I, Mat. Mekh. Astron. 2009, No. 4, 20--27 (2009)]. Due to the bounded differentiability of the introduced functions, the degree of the polynomial replacement must be limited. The system of differential equations for the replacement coefficients is solved recursively. The number of found Lyapunov constants is also bounded. This paper considers the in which when all found constants are zero. To study this problem, a method is used of isolating the main part of the introduced functions and their combinations as a result of the expansion of the latter in the Fourier series. The remainder of the series is assumed to be rather small, and it is shown that its presence can be neglected. The transition to the main parts instead of functions allows the lack of differentiability of the introduced functions to be compensated. In the case of such systems, polynomial replacement can be again used and the Lyapunov constant for each main part can be found. It is shown that the sign of the constant for any main part is preserved. Sufficient conditions for stability and instability are indicated. Other relevant input to this research is found in [\textit{L. D. Kudryavtsev}, A course in mathematical analysis. Vol. 1. Textbook. (Kurs matematicheskogo analiza. Tom 1. Uchebnik) (Russian). Ministerstvo Vysshego i Srednego Spetsial'nogo Obrazovaniya SSSR. Moskva: ``Vysshaya Shkola'' (1981; Zbl 0485.26001); A course in mathematical analysis. Vol. II. Textbook. (Kurs matematicheskogo analiza. Tom II. Uchebnik) (Russian). Ministerstvo Vysshego i Srednego Spetsial'nogo Obrazovaniya SSSR. Moskva: ``Vysshaya Shkola'' (1981; Zbl 0485.26002)].
Reviewer: Adeleke Timothy Ademola (Ile-Ife)Stability analysis for time-varying nonlinear systemshttps://zbmath.org/1500.340492023-01-20T17:58:23.823708Z"Taieb, Nizar Hadj"https://zbmath.org/authors/?q=ai:taieb.nizar-hadjSummary: This paper is concerned with practical asymptotic and exponential stability analysis of time-varying nonlinear systems. With the help of the new notion of practical stable functions, some differential Lyapunov inequalities based necessary and sufficient conditions are derived for testing global uniform practical asymptotic stability and practical exponential stability of general time-varying nonlinear systems. Therefore, we generalised some works which are already made in the literature. Furthermore, some illustrative examples are presented.Pseudoholomorphic and \(\varepsilon \)-pseudoregular solutions of singularly perturbed problemshttps://zbmath.org/1500.340502023-01-20T17:58:23.823708Z"Kachalov, V. I."https://zbmath.org/authors/?q=ai:kachalov.vasily-ivanovichSummary: For nonlinear evolution equations in a Banach space that depend in two ways -- regularly and singularly -- on a small parameter, we construct \(\varepsilon \)-pseudoregular solutions of the Cauchy problem, i.e., its formal solutions representable as series in powers of the small parameter with coefficients that depend on it in a singular way and converging in a certain neighborhood of the zero value of the parameter uniformly over a given time interval. Sufficient conditions are obtained under which the sum of such a series is an exact, and hence pseudoholomorphic, solution of this problem.Stochastic resonance in a fractional oscillator with cross-correlation noisehttps://zbmath.org/1500.340512023-01-20T17:58:23.823708Z"Ou, Hong-Lei"https://zbmath.org/authors/?q=ai:ou.hong-lei"Ren, Ruibin"https://zbmath.org/authors/?q=ai:ren.ruibin"Deng, Ke"https://zbmath.org/authors/?q=ai:deng.keSummary: For an over-damped linear system with fractional derivative driven by both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we investigate the stochastic resonance phenomenon in this paper. Applying the Shapiro-Loginov formula and the generalized harmonic function approach, we obtain the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, the signal-to-noise ratio for the system is obtained. We find that the time-periodic modulation intensity between noises diversifies the stochastic resonance phenomenon and makes the system possess richer dynamic behaviors.Bounded solutions of evolutionary equations. Ihttps://zbmath.org/1500.340522023-01-20T17:58:23.823708Z"Bihun, D. S."https://zbmath.org/authors/?q=ai:bihun.d-s"Pokutnyi, O. O."https://zbmath.org/authors/?q=ai:pokutnij.olexandr-o"Kliuchnyk, I. G."https://zbmath.org/authors/?q=ai:kliuchnyk.i-g"Sadovyi, M. I."https://zbmath.org/authors/?q=ai:sadovyi.m-i"Tryfonova, O. M."https://zbmath.org/authors/?q=ai:tryfonova.o-mAs one of main problems in the qualitative theory of differential equations, it can be mentioned the problem of behavior of solutions at infinity. A class of systems whose solutions may both vanish with exponential speed and infinitely increase are analyzed with the help of the concept of exponential dichotomy on all axes and semiaxes of the considered system. In this work, the authors treat numerous results on the existence of bounded solutions of linear and nonlinear abstract differential equations accumulated by the authors for the last years and some new results obtained under the condition of exponential dichotomy, \(\mu\)-dichotomy, and \(\nu\)-dichotomy of the corresponding linear homogeneous equation. The authors also present examples to illustrate the theory to the study of specific differential equations and systems of differential equations in Banach and Frechet spaces, as well as in general locally convex topological spaces. Moreover, some results from the theory of almost periodic solutions of operator-differential equations are also given.
Reviewer: Ismail Huseynov (Mersin)Uniqueness criterion for solutions of nonlocal problems on a finite interval for abstract singular equationshttps://zbmath.org/1500.340532023-01-20T17:58:23.823708Z"Glushak, A. V."https://zbmath.org/authors/?q=ai:glushak.a-vLet \(E\) be a complex Banach space and let \(A,B\) be linear closed operators on \(E\) whose domains are not necessary dense. Consider the equation
\[
B(u''(t)+\frac{k}{t}u'(t))=Au(t),\quad 0<t<1.
\]
The following cases are considered
\begin{itemize}
\item \(k\geq0\) with Neumann boundary condition \(u'(0)=0\) and non-local condition
\(\int_0^1t^k(1-t^2)^{\alpha-1}u(t)dt=0\) (\(\alpha>0\))
\item \(k<1\) with Dirichlet boundary condition \(u(0)=0\) and non-local condition
\(\int_0^1t(1-t^2)^{\beta-1}u(t)dt=0\) (\(\beta>0\))
\item \(k\geq0\) with Neumann boundary condition \(u'(0)=0\) and non-local condition
\(a\int_0^1t^ku(t)dt+bu'(1)=0\) (\(a,b\ne0\))
\item \(k<1\) with Dirichlet boundary condition \(u(0)=0\) and non-local condition
\(a\int_0^1t^ku(t)dt+b\lim_{t\to1}(t^{k-1}u(t))'=0\)
\end{itemize}
For each case a uniqueness criterion is established.
Applications to the equation \(t^\gamma v''+bt^{\gamma-1}v'=Av\) are given.
Reviewer: Nikita V. Artamonov (Moskva)Stability of mild solutions of the fractional nonlinear abstract Cauchy problemhttps://zbmath.org/1500.340542023-01-20T17:58:23.823708Z"Vanterler da Costa Sousa, J."https://zbmath.org/authors/?q=ai:vanterler-da-costa-sousa.jose"Kucche, Kishor D."https://zbmath.org/authors/?q=ai:kucche.kishor-d"de Oliveira, E. Capelas"https://zbmath.org/authors/?q=ai:de-oliveira.edmundo-capelasIn this paper, the authors mainly consider the stability of mild solutions of fractional nonlinear differential equations, including the Ulam-Hyers stability and Ulam-Hyers-Rassias stability. In view of the theory of resolvent operator families, the expressions of mild solutions are given in the first part. Then, according to the definitions of stability and to the fixed point approach, stability results are derived in the second part of this paper. In particular, the authors obtain the stability of mild solutions of fractional differential equations on the finite and infinite intervals, respectively. These results contribute to the theory of stability of fractional nonlinear differential equations.
Reviewer: Zhenbin Fan (Jiangsu)Correct restrictions of first-order functional-differential equationhttps://zbmath.org/1500.340552023-01-20T17:58:23.823708Z"Akhymbek, Meiram E."https://zbmath.org/authors/?q=ai:akhymbek.meiram-erkanatuly"Sadybekov, Makhmud A."https://zbmath.org/authors/?q=ai:sadybekov.makhmud-abdysametovich|sadybekov.makhmud-aSummary: The main purpose of this article is describing all the correct restrictions of maximal operator \(L_{ max }\) which are given by a functional-differential equation \(L_{ max }u(x) = u'(x) + au '(1 - x), 0 < x < 1\), with domain \(D(L_{\max}) = W_2^1(0, 1)\), where \(a\) is a fixed number.
For the entire collection see [Zbl 1436.46003].Odd-order differential equations with deviating arguments: asymptomatic behavior and oscillationhttps://zbmath.org/1500.340562023-01-20T17:58:23.823708Z"Muhib, A."https://zbmath.org/authors/?q=ai:muhib.ali"Dassios, I."https://zbmath.org/authors/?q=ai:dassios.ioannis-k"Baleanu, D."https://zbmath.org/authors/?q=ai:baleanu.dumitru-i"Santra, S. S."https://zbmath.org/authors/?q=ai:santra.shyam-sundar"Moaaz, O."https://zbmath.org/authors/?q=ai:moaaz.osamaIn this paper, the authors discuss the nonoscillatory and asymptotic behavior of delay differential equations of odd-order
\[
(a(\eta)(\psi^{(n-1) }(\eta))^{\kappa})'+q(\eta)f(\psi(\phi(\eta)))=0\tag{1.1}
\]
and
\[
\left(a(\eta)\left(v^{(n-1) }(\eta)\right)^{\kappa}\right)'+q(\eta)f(\psi(\phi(\eta)))=0, \quad v(\eta)=\psi(\eta)+p(\eta)\psi(\tau(\eta))\quad \tag{1.2}
\]
under the assumption that \(n\ge 3\) is an odd integer;
\begin{itemize}
\item[(i)] \(\kappa\) is the ratio of odd natural numbers;\\
\item[(ii)] \(q, p\in C([\eta_{0},\infty),(0,\infty))\) and \(0\le p(\eta)<1\);\\
\item[(iii)] \(a,\tau,\phi \in C^{1}([\eta_{0},\infty))\), \(a(\eta)>0\), \(a'(\eta)\ge0\), \(\phi(\eta) \ge \eta \ge \tau(\eta)\), \(\lim_{\eta\to\infty}\tau(\eta)=\infty\);\\
\item[(iv)] \(f \in C(\mathbb{R}, \mathbb{R})\), \(f(\psi)\ge k\psi^{\kappa}\) and \[\pi(\eta)=\int_{\eta_{0}}^{\eta}\dfrac{1}{a^{1/\kappa}(s)}\text{d}s \to \infty \quad \text{as} \quad \eta \to \infty.\]
\end{itemize}
The authors provide sufficient conditions which guarantee that every nonoscillatory solution \(\psi(\eta)\) of (1.1) and (1.2) satisfy \(\lim_{\eta \to \infty}\psi(\eta)=0\) (see Theorems 3.1 and 3.2). The authors also derive results on the asymptotic behavior of the nonoscillatory solution of (1.2) (see Theorems 3.3 and 3.4). To prove the results, the authors use Riccati transformation and some analytical skill.
Reviewer: Kazuki Ishibashi (Hiroshima)Periodic solutions of impulsive differential equations with piecewise alternately advanced and retarded argument of generalized typehttps://zbmath.org/1500.340572023-01-20T17:58:23.823708Z"Chiu, Kuo-Shou"https://zbmath.org/authors/?q=ai:chiu.kuo-shouThe paper investigates the nonlinear vector impulsive system
\[
\dot{y}(t)=A(t)y(t)+f(t,y(t), y(\gamma(t))),
\]
\[ \Delta y(t)=J_k(y(t_k^-)), t=t_k, k\in Z,
\]
where \(\gamma(t)\) is a piecewise constant argument of mixed type (alternatively delayed or advanced).
The existence and uniqueness of periodic and subharmonic solutions are obtained by applying the Poincaré operator and fixed point theory.
Reviewer: Leonid Berezanski (Be'er Sheva)Non-autonomous differential systems with delays: a global attraction analysishttps://zbmath.org/1500.340582023-01-20T17:58:23.823708Z"Ruiz-Herrera, Alfonso"https://zbmath.org/authors/?q=ai:ruiz-herrera.alfonsoAuthor's abstract: In this paper, we derive criteria of global attractivity of a (possibly constant) positive periodic solution in non-autonomous systems of delay differential equations. Our approach can be viewed as the extension for non-autonomous systems of the folkloric connection between discrete dynamics and scalar delay differential equations. It is worth mentioning that we provide delay-dependent criteria of global attraction that cover the best delay independent conditions. We apply our results to non-autonomous variants of several classical models such that Nicholson's blowfly equation, Goodwin's model oscillator, the Mackey-Glass equation and systems with patch structure.
Reviewer: Eric R. Kaufmann (Little Rock)Periodic perturbations of a class of functional differential equationshttps://zbmath.org/1500.340592023-01-20T17:58:23.823708Z"Spadini, Marco"https://zbmath.org/authors/?q=ai:spadini.marcoIn this paper, the author studies the existence of a connected ``branch'' of periodic solutions of \(T\)-periodic perturbations of a particular class of functional differential equations on differentiable manifolds. Their result is obtained by a combination of degree-theoretic methods and a technique that allows to associate the bounded solutions of the functional equation to bounded solutions of a suitable ordinary differential equation.
The author develops their analysis using methods inspired by \textit{M. Furi} et al. [in: Handbook of topological fixed point theory. Berlin: Springer. 741--782 (2005; Zbl 1089.47046); \textit{M. Furi} and \textit{M. Spadini}, Nonlinear Anal., Theory Methods Appl. 29, No. 8, 963--970 (1997; Zbl 0885.34041)]. However, the techniques developed in those papers do not apply directly to perturbations of general functional differential equations but, for the particular form the author observes that the study of periodic solutions can be reduced to the study of the periodic solution of an ordinary differential equation on a higher dimensional manifold. The authors point out that, at the price of some more minor technicalities, the same ``reduction'' strategy adopted in this paper could be applied to the more general case when the periodic perturbation depends also on a retarded term, with delay that might be fixed or functional (possibly infinite).
Reviewer: Yingxin Guo (Qufu)Hopf bifurcation of a fractional tri-neuron network with different orders and leakage delayhttps://zbmath.org/1500.340602023-01-20T17:58:23.823708Z"Wang, Yangling"https://zbmath.org/authors/?q=ai:wang.yangling"Cao, Jinde"https://zbmath.org/authors/?q=ai:cao.jinde"Huang, Chengdai"https://zbmath.org/authors/?q=ai:huang.chengdaiSummary: This paper focuses on the Hopf bifurcation of a fractional tri-neuron network with both leakage delay and communication delay under different fractional orders. By applying fractional Laplace transform, the stability theorem of linear autonomous system and Hopf bifurcation theorem, we obtain a class of asymptotic stability criterion of zero solution as well as delay-induced Hopf bifurcation conditions for the considered system. Simultaneously, the stability and Hopf bifurcation for tri-neuron network with single fractional order are also discussed as a special case of our proposed neural network model. Finally, a simulation example is given to illustrate the efficiency of the presented theoretical results in this paper.On stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controlshttps://zbmath.org/1500.340612023-01-20T17:58:23.823708Z"Čermák, Jan"https://zbmath.org/authors/?q=ai:cermak.jan"Nechvátal, Luděk"https://zbmath.org/authors/?q=ai:nechvatal.ludekAuthors' abstract: The paper discusses stabilizing effects of some time-delayed feedback controls applied to unstable steady states of an autonomous system of ordinary differential equations. First, we derive explicit delay-dependent stability conditions that are applicable to a family of time-delayed systems with simultaneously triangularizable system matrices. Then, using this criterion and other argumentation, we employ diagonal delayed feedback controls of conventional and Pyragas-type to stabilize unstable steady states of the studied autonomous system. More precisely, we formulate explicit, non-improvable and immediately applicable conditions on time delay and feedback strength that enable such a stabilization. As an illustration, we stabilize the unstable steady states of the Rössler dynamical system considered under the standard choice of entry parameters when the uncontrolled system displays a chaotic behavior. Also, we consider a non-diagonal feedback control (whose rotational gain matrix, involving a feedback strength and phase, commutes with the Jacobi matrix of the uncontrolled system) and show its larger stabilization potential with respect to the appropriate diagonal control. The obtained results are tested by numerical experiments and confronted with the existing results. As a supplement, we provide MATLAB codes supporting theoretical conclusions.
Reviewer: Serhiy Yanchuk (Berlin)Dynamics of a third order differential equation with piecewise constant argument of generalized typehttps://zbmath.org/1500.340622023-01-20T17:58:23.823708Z"Çinçin, Duygu Aruğaslan"https://zbmath.org/authors/?q=ai:arugaslan-cincin.duygu"Cengiz, Nur"https://zbmath.org/authors/?q=ai:cengiz.nurSummary: In this work, we address a third order differential equation with generalized piecewise constant argument. Investigation concerning the existence, uniqueness of the solutions of the equation is performed. Sufficient conditions that guarantee the existence of uniformly asymptotically stable trivial solution are given on the basis of both Lyapunov-Krasovskii and Lyapunov-Razumikhin methods. The results are supported by an example and a simulation.Impulsive differential equations involving general conformable fractional derivative in Banach spaceshttps://zbmath.org/1500.340632023-01-20T17:58:23.823708Z"Liang, Jin"https://zbmath.org/authors/?q=ai:liang.jin"Mu, Yunyi"https://zbmath.org/authors/?q=ai:mu.yunyi"Xiao, Ti-Jun"https://zbmath.org/authors/?q=ai:xiao.ti-junSummary: This paper deals with two classes of impulsive equations involving the general conformable fractional derivative in Banach spaces: (1) impulsive Sobolev-type integro-differential equations with the general conformable fractional derivative, (2) impulsive delay evolution equations with the general conformable fractional derivative. By combining the generalized Laplace transform and the properties of the general conformable fractional derivative, we present a proper definition of mild solutions for the impulsive integro-differential equations with the general conformable fractional derivative. In view of this definition, we obtain a new existence theorem of \((\omega, c)\)-periodic solutions for a normal fractional inhomogeneous evolution equation with the general conformable fractional derivative (Theorem 2.3) which will be used to study the \((\omega, c)\)-periodic solutions for the impulsive delay evolution equations with the general conformable fractional derivative. Then we establish existence and uniqueness theorems for the impulsive integro-differential equations with the general conformable fractional derivative. Next, we derive existence theorems of \((\omega, c)\)-periodic solutions for the impulsive delay evolution equations involving the general conformable fractional derivative. Finally, applications are also given to illustrate our abstract results.Well-posedness and dynamics of double time-delayed lattice FitzHugh-Nagumo systemshttps://zbmath.org/1500.340642023-01-20T17:58:23.823708Z"Zhang, Qiangheng"https://zbmath.org/authors/?q=ai:zhang.qianghengIn this paper the author studies the well-posedness and dynamics of FitzHugh-Nagumo systems with variable delay defined on infinite lattices. First the author proves the existence and uniqueness of solutions as well as the existence of an evolution process for this system, then established the existence of tempered pullback attractors and invariant measures. Finally, the author studied the upper semicontinuity of pullback attractors as the delay time tends to zero.
Reviewer: Xiong Li (Beijing)Stability and asymptotically periodic solutions of hybrid systems with aftereffecthttps://zbmath.org/1500.340652023-01-20T17:58:23.823708Z"Simonov, P. M."https://zbmath.org/authors/?q=ai:simonov.pyotr-mikhailovich|simonov.petr-mSummary: In this paper, we study hybrid linear systems of functional differential equations with aftereffect using the \(W\)-method proposed by N. V. Azbelev. Two model equations are considered. We examine Banach spaces of right-hand sides and solutions of the equations considered; these spaces consist of asymptotically periodic functions. Analogs of the Bohl-Perron theorem on the asymptotic stability and on the existence of limits of solutions are obtained.The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: when delay-systems characteristics meet the zeros of Kummer functionshttps://zbmath.org/1500.340662023-01-20T17:58:23.823708Z"Boussaada, Islam"https://zbmath.org/authors/?q=ai:boussaada.islam"Mazanti, Guilherme"https://zbmath.org/authors/?q=ai:mazanti.guilherme"Niculescu, Silviu-Iulian"https://zbmath.org/authors/?q=ai:niculescu.silviu-iulianThe paper is devoted to investigation of a time-delay system. The structure of the paper is as follows. First, the autors present some prerequisites in complex analysis. Then, they show the validity of the generic multiplicity-induced-dominancy property for linear functional differential equations with a single delay, including the retarded as well as the neutral types. Further, the general results are illustrated on the problem of stabilization of the classical pendulum and the feedback stabilization for a scalar conservation law with proportional-integral (PI) boundary control.
Reviewer: Vyacheslav I. Maksimov (Yekaterinburg)Finite-time stability results for fractional damped dynamical systems with time delayshttps://zbmath.org/1500.340672023-01-20T17:58:23.823708Z"Arthi, Ganesan"https://zbmath.org/authors/?q=ai:arthi.ganesan"Brindha, Nallasamy"https://zbmath.org/authors/?q=ai:brindha.nallasamy"Baleanu, Dumitru"https://zbmath.org/authors/?q=ai:baleanu.dumitru-iSummary: This paper is explored with the stability procedure for linear nonautonomous multiterm fractional damped systems involving time delay. Finite-time stability (FTS) criteria have been developed based on the extended form of Gronwall inequality. Also, the result is deduced to a linear autonomous case. Two examples of applications of stability analysis in numerical formulation are described showing the expertise of theoretical prediction.Multidelay differential equations: a Taylor expansion approachhttps://zbmath.org/1500.340682023-01-20T17:58:23.823708Z"Doldo, Philip"https://zbmath.org/authors/?q=ai:doldo.philip"Pender, Jamol"https://zbmath.org/authors/?q=ai:pender.jamolIn this paper a neutral delay differential equation (DDE) with only a single constant delay is studied. In order to approximate the change in stability in multidelay system the authors derive a critical delay in the neutral DDE via a Taylor expansion. Moreover, DDE with a single constant delay that has a delayed second-derivative term is presented and its critical delay is obtained. Analysis of the above approximations is developed for a two-delay system. The results presented in the paper may have applications in queueing systems in order to obtain updated waiting time or queue length information.
Reviewer: Angela Slavova (Sofia)A remark of \(k\)-summability of divergent solutions to some linear \(q\)-difference-differential equations with entire Cauchy datahttps://zbmath.org/1500.340692023-01-20T17:58:23.823708Z"Ichinobe, Kunio"https://zbmath.org/authors/?q=ai:ichinobe.kunioSummary: We consider the Cauchy problem (CP) to some linear \(q\)-difference-differential equations with entire Cauchy data. We see that the summability condition is equivalent with the convergence for the formal solution in some case.
For the entire collection see [Zbl 1484.34002].Besicovitch almost periodic solutions to stochastic dynamic equations with delayshttps://zbmath.org/1500.340702023-01-20T17:58:23.823708Z"Li, Yongkun"https://zbmath.org/authors/?q=ai:li.yongkun|li.yongkun.1"Huang, Xiaoli"https://zbmath.org/authors/?q=ai:huang.xiaoliSummary: In order to unify the study of Besicovitch almost periodic solutions of continuous time and discrete-time stochastic differential equations, we first propose concepts of Besicovitch almost periodic stochastic processes in \(p\)-th mean and of Besicovitch almost periodic stochastic processes in distribution on time scales, and reveal the relationship between the two random processes. Then, taking a class of stochastic Clifford-valued neural networks with time-varying delays on time scales as an example of stochastic dynamic equations with delays, we establish the existence and stability of Besicovitch almost periodic solutions in distribution for this class of networks by using Banach's fixed point theorem, time scale calculus theory and inequality techniques.The criteria for oscillation of two-dimensional neutral delay dynamical systems on time scaleshttps://zbmath.org/1500.340712023-01-20T17:58:23.823708Z"Sun, Zhongfeng"https://zbmath.org/authors/?q=ai:sun.zhongfeng"Qin, Huizeng"https://zbmath.org/authors/?q=ai:qin.huizengThis paper investigates the oscillation of the neutral delay system
\[
\begin{cases}
z^{\Delta}(t) = b(t)g\{r(t)\psi[x(t)] y[\eta(t)]\}, \\
y^{\Delta}(t) = - f (t, x[\delta(t)])
\end{cases}
\]
on time scales. Utilizing Lemma 1, the integral oscillation condition
\[
\int_{t_0}^\infty f(s,c(1-p[\delta(s)])\Delta s=\infty \quad \forall c>0
\]
is obtained in Theorem 2, which is subsequently improved under additional assumptions in Theorems 3--6, Lemma 7. Corollaries are obtained in the special case of
\[
\begin{cases}
x^\Delta(t)=a^{-(1/\alpha)}(t) |y(t)|^{(1/\alpha)-1} y(t), \\
y^\Delta(t)=-f(t,x[\sigma(t)]).
\end{cases}
\]
Theorem 8 guarantees oscillation under some special conditions. Question: Can the $b(t)$ term be eliminated from the equation, with its non-monotonous nature taken into account by an appropriate transformation of $r(t)$? Such a transformation could simplify conditions A3, A4.
Reviewer: Ioannis P. Stavroulakis (Ioannina)Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategyhttps://zbmath.org/1500.340722023-01-20T17:58:23.823708Z"Hikal, M. M."https://zbmath.org/authors/?q=ai:hikal.manal-m"Elsheikh, M. M. A."https://zbmath.org/authors/?q=ai:elsheikh.m-m-a"Zahra, W. K."https://zbmath.org/authors/?q=ai:zahra.waheed-k(no abstract)A graph-theoretic condition for delay stability of reaction systemshttps://zbmath.org/1500.340732023-01-20T17:58:23.823708Z"Yu, Polly Y."https://zbmath.org/authors/?q=ai:yu.polly-y"Craciun, Gheorghe"https://zbmath.org/authors/?q=ai:craciun.gheorghe"Mincheva, Maya"https://zbmath.org/authors/?q=ai:mincheva.maya"Pantea, Casian"https://zbmath.org/authors/?q=ai:pantea.casian-alexandruAuthors' abstract: Delay mass-action systems provide a model of chemical kinetics when past states influence the current dynamics. In this work, we provide a graph-theoretic condition for delay stability, i.e., linear stability independent of both rate constants and delay parameters. In particular, the result applies when the system has no delay, implying asymptotic stability for the ODE system. The graph-theoretic condition is about cycles in the directed species-reaction graph of the network, which encodes how different species in the system interact.
Reviewer: Krishnan Balachandran (Coimbatore)Dynamic analysis of a fractional-order SIRS model with time delayhttps://zbmath.org/1500.340742023-01-20T17:58:23.823708Z"Zhou, Xueyong"https://zbmath.org/authors/?q=ai:zhou.xueyong"Wang, Mengya"https://zbmath.org/authors/?q=ai:wang.mengyaSummary: Mathematical modeling plays a vital role in the epidemiology of infectious diseases. Policy makers can provide the effective interventions by the relevant results of the epidemic models. In this paper, we build a fractional-order SIRS epidemic model with time delay and logistic growth, and we discuss the dynamical behavior of the model, such as the local stability of the equilibria and the existence of Hopf bifurcation around the endemic equilibrium. We present the numerical simulations to verify the theoretical analysis.Algebraic, rational and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension onehttps://zbmath.org/1500.340752023-01-20T17:58:23.823708Z"Cano, José"https://zbmath.org/authors/?q=ai:cano.jose-maria"Falkensteiner, Sebastian"https://zbmath.org/authors/?q=ai:falkensteiner.sebastian"Sendra, J. Rafael"https://zbmath.org/authors/?q=ai:sendra.juan-rafaelSummary: In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain type of systems of autonomous ordinary differential equations. More precisely, we deal with systems which associated algebraic set is of dimension one. We establish a relationship between the solutions of the system and the solutions of an associated first order autonomous ordinary differential equation, that we call the reduced differential equation. Using results on such equations, we prove the convergence of the formal Puiseux series solutions of the system, expanded around a finite point or at infinity, and we present an algorithm to describe them. In addition, we bound the degree of the possible algebraic and rational solutions, and we provide an algorithm to decide their existence and to compute such solutions if they exist. Moreover, if the reduced differential equation is non trivial, for every given point \((x_0,y_0) \in \mathbb{C}^2\), we prove the existence of a convergent Puiseux series solution \(y(x)\) of the original system such that \(y(x_0)=y_0\).On a general singular solution of the fifth Painlevé equation along the positive real axishttps://zbmath.org/1500.340762023-01-20T17:58:23.823708Z"Shimomura, Shun"https://zbmath.org/authors/?q=ai:shimomura.shunIn this paper, the author studies the fifth Painlevé equation \(P_V\)
\[
\begin{aligned}
\frac{d^2 y}{d t^2}=\left(\frac{1}{2 y} +\frac{1}{y-1}\right)\left(\frac{dy}{d
t}\right)^2-\frac{1}{t}\frac{dy}{d t}+\\
+\frac{(y-1)^2}{8 t^2}
\left((\theta_0-\theta_1+\theta_{\infty})^2 y -\frac{(\theta_0-\theta_1-\theta_{\infty})^2}{y}\right)\\
+ (1-\theta_0-\theta_1)\frac{y}{t} - \frac{y (y+1)}{2 (y-1)}
\end{aligned}
\]
when \(\theta_0-\theta_1=\theta_{\infty}=0\) and the variable \(t\) is real and positive. In particular, he intoduces a system of non-linear equations that is equivalent to the \(P_V\) and arises from a study of the elliptic asymptotic representation of a generic solution of \(P_V\) [\textit{S. Shimomura}, Kyushu J. Math. 76, No. 1, 43--99 (2022; Zbl 07545407)]. The author finds a two-parameter family of asymptotic solutions of this system and proves that this solution coincides on a special domain with the general singular solution of \(P_V\) given by \textit{F. V. Andreev} and \textit{A. V. Kitaev} [Nonlinearity 13, No. 5, 1801--1840 (2000; Zbl 0970.34076)]. The author also presents explicitly the error term of the obtained solution and poses a conjecture on the asymptotic expansion of the error term.
Reviewer: Tsvetana Stoyanova (Sofia)Exact WKB analysis of the hypergeometric differential equation with a simple polehttps://zbmath.org/1500.340772023-01-20T17:58:23.823708Z"Takahashi, Toshinori"https://zbmath.org/authors/?q=ai:takahashi.toshinori"Tanda, Mika"https://zbmath.org/authors/?q=ai:tanda.mikaSummary: The Gauss hypergeometric differential equation with a large parameter deformed to a differential equation with a simple pole at the origin is considered. The relations between Kummer's solutions in the neighborhood of the regular singular point \(1\) and the Borel sums of the WKB solutions are established.
For the entire collection see [Zbl 1484.34002].Local and non-local improved Hardy inequalities with weightshttps://zbmath.org/1500.350062023-01-20T17:58:23.823708Z"Canale, Anna"https://zbmath.org/authors/?q=ai:canale.annaSummary: The main result in this paper is an improved Hardy inequality for functions in weighted Sobolev spaces, for a class of potentials that perturbs the inverse square potentials and for weight functions satisfying the Hölder condition. As a consequence, we derive some local improved Hardy inequalities.
An application to evolution problems with Kolmogorov operators is shown.Instability of mixing in the Kuramoto model: from bifurcations to patternshttps://zbmath.org/1500.350252023-01-20T17:58:23.823708Z"Chiba, Hayato"https://zbmath.org/authors/?q=ai:chiba.hayato"Medvedev, Georgi S."https://zbmath.org/authors/?q=ai:medvedev.georgi-s"Mizuhara, Matthew S."https://zbmath.org/authors/?q=ai:mizuhara.matthew-sSummary: We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which can also be random. We show that the emergent patterns are formed via two independent mechanisms determined by the shape of the frequency distribution and the limiting structure of the underlying graph sequence. Specifically, we identify two nested eigenvalue problems whose eigenvectors (unstable modes) determine the structure of the nascent patterns. The latter include stationary and travelling clusters, twisted states, chimera states and combinations of the above. In contrast to reaction-diffusion systems, where patterns are expressed by smooth solutions, they are served by tempered distributions for the model at hand. The analysis is illustrated with the result of the numerical experiments with the Kuramoto model with unimodal and bimodal frequency distributions on certain graphs.Controller and asymptotic autonomy of random attractors for stochastic p-Laplace lattice equationshttps://zbmath.org/1500.350532023-01-20T17:58:23.823708Z"Song, Li"https://zbmath.org/authors/?q=ai:song.li"Li, Yangrong"https://zbmath.org/authors/?q=ai:li.yangrong"Wang, Fengling"https://zbmath.org/authors/?q=ai:wang.fenglingSummary: A non-autonomous random dynamical system is called to be controllable if there is a pullback random attractor (PRA) such that each fibre of the PRA converges upper semi-continuously to a nonempty compact set (called a controller) as the time-parameter goes to minus infinity, while the PRA is called to be asymptotically autonomous if there is a random attractor for another (autonomous) random dynamical system as a controller. We establish the criteria for ensuring the existence of the minimal controller and the asymptotic autonomy of a PRA respectively. The abstract results are illustrated in possibly non-autonomous stochastic p-Laplace lattice equations with tempered convergent external forces.Exact solutions of the \((2+1)\)-dimensional Kundu-Mukherjee-Naskar model via IBSEFMhttps://zbmath.org/1500.350832023-01-20T17:58:23.823708Z"Mamedov, Kh. R."https://zbmath.org/authors/?q=ai:mamedov.khanlar-rashid|mamedov.khanlar-r"Demirbilek, U."https://zbmath.org/authors/?q=ai:demirbilek.ulviye"Ala, V."https://zbmath.org/authors/?q=ai:ala.volkanSummary: The aim of this study is to construct the exact solutions of the \((2+1)\)-dimensional Kundu-Mukherjee-Naskar (KMN) equation via Improved Bernoulli Sub-Equation Function Method (IBSEFM). The physics of this model describes optical dromions in \((2+1)\)-dimensional case. It is also studied in fluid dynamics. Applying the proposed method, we obtain new exact solutions of \((2+1)\)-dimensional KMN equation. Moreover, we plot the 2D--3D figures and contour surfaces according to the suitable parameters by the aid of computer software. The results confirm that IBSEFM is powerful, effective and straightforward for solving nonlinear partial differential equations arising in mathematical physics.The analysis of solitonic, supernonlinear, periodic, quasiperiodic, bifurcation and chaotic patterns of perturbed Gerdjikov-Ivanov model with full nonlinearityhttps://zbmath.org/1500.352712023-01-20T17:58:23.823708Z"Rafiq, Muhammad Hamza"https://zbmath.org/authors/?q=ai:rafiq.muhammad-hamza"Jhangeer, Adil"https://zbmath.org/authors/?q=ai:jhangeer.adil"Raza, Nauman"https://zbmath.org/authors/?q=ai:raza.naumanSummary: In this manuscript, the perturbed Gerdjikov-Ivanov equation is considered for the investigating model. It is studied to govern the dynamics of soliton propagation through optical fibers, metamaterials or PCF. The observed model is subjected to an extended simple equation technique, which disclosed an abundant of exact solutions including trigonometric function, singular, kink, peakon and compacton solutions. These solutions are made available with their essential conditions, which guarantee the persistence of such optical solitons and portraits using appropriate physical parameters in 3D, 2D and density plots. After that, the traveling wave transformation is used to turn the \(m t h\)-order nonlinear perturbed Gerdjikov-Ivanov equation into a planar dynamical system. The dynamical and chaotic behaviors of the considered equation are also discussed. The qualitative analysis of the dynamical system and the chaotic behaviors of the perturbed system are investigated using the theory of plane dynamic systems. In addition, we utilize the RK4 method to discover patterns in the dynamical system that seem to be super nonlinear, periodic, and quasiperiodic. The reported results are new and have not been investigated. They can be used in the explanation of the physical phenomena modeled and will give information about the long-term dynamic behavior. Numerical simulations reveal that by changing the frequency and amplitude parameters have an impact on the dynamic behaviors of the system. It is established that the extended simple equation method and dynamical observations offer further influential mathematical tools for constructing exact solutions and their qualitative analysis in NLEEs in mathematical physics.Brouwer degree for mean field equation on graphhttps://zbmath.org/1500.352842023-01-20T17:58:23.823708Z"Liu, Yang"https://zbmath.org/authors/?q=ai:liu.yang.63|liu.yang.19|liu.yang.22|liu.yang.18|liu.yang.5|liu.yang.13|liu.yang.7|liu.yang.17|liu.yang|liu.yang.10|liu.yang.12|liu.yang.26|liu.yang.8|liu.yang.9|liu.yang.16|liu.yang.4|liu.yang.25|liu.yang.11|liu.yang.3|liu.yang.1|liu.yang.14|liu.yang.21|liu.yang.2Summary: Let \(u\) be a function on a connected finite graph \(G=(V, E)\). We consider the mean field equation
\[
-\Delta u=\rho\bigg( \frac{he^u}{\int_V he^u d\mu}-\frac{1}{|V|}\bigg),
\tag{1}
\]
where \(\Delta\) is \(\mu\)-Laplacian on the graph, \(\rho\in \mathbb{R}\backslash\{ 0\},\; h: V\rightarrow\mathbb{R^+}\) is a function satisfying \(\min_{x\in V}h(x)>0\). Following \textit{L. Sun} and \textit{L. Wang} [Adv. Math. 404, Part B, Article ID 108422, 29 p. (2022; Zbl 1490.35512)], we use the method of Brouwer degree to prove the existence of solutions to the mean field equation (1). Firstly, we prove the compactness result and conclude that every solution to the equation is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation (1), say
\[
d_{\rho,h} =
\begin{cases}
-1, & \rho >0, \\
1, & \rho <0.
\end{cases}
\]
Consequently, the equation (1) has at least one solution due to the Brouwer degree \(d_{\rho,h}\neq 0\).On a problem for the nonlinear diffusion equation with conformable time derivativehttps://zbmath.org/1500.352912023-01-20T17:58:23.823708Z"Au, Vo Van"https://zbmath.org/authors/?q=ai:au.vo-van"Baleanu, Dumitru"https://zbmath.org/authors/?q=ai:baleanu.dumitru-i"Zhou, Yong"https://zbmath.org/authors/?q=ai:zhou.yong.1"Huu Can, Nguyen"https://zbmath.org/authors/?q=ai:can.nguyen-huuSummary: In this paper, we study a nonlinear diffusion equation with conformable derivative: \(\mathfrak{D}_t^{(\alpha)} u - \Delta u = \mathcal{L}(x,t; u(x,t))\), where \(0 < \alpha <1, (x,t) \in \Omega \times (0,T)\). We consider both of the problems:
\begin{enumerate}
\item[\(\bullet\)] Initial value problem: the solution contains the integral \(I = \int_0^t \tau^\gamma \mathrm{d}\tau\) (critical as \(\gamma \leq -1)\).
\item[\(\bullet\)] Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data).
\end{enumerate}
For the initial value problem, the lack of convergence of the integral \(I\), for \(\gamma \leq -1\). The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.On spectral and fractional powers of damped wave equationshttps://zbmath.org/1500.352932023-01-20T17:58:23.823708Z"Belluzi, Maykel"https://zbmath.org/authors/?q=ai:belluzi.maykel"Bezerra, Flank D. M."https://zbmath.org/authors/?q=ai:bezerra.flank-david-morais"Nascimento, Marcelo J. D."https://zbmath.org/authors/?q=ai:nascimento.marcelo-jose-diasSummary: In this paper we explore the theory of fractional powers of positive operators, more precisely, we use the Balakrishnan formula to obtain parabolic approximations of (damped) wave equations in bounded smooth domains in \(\mathbb{R}^N\). We also explicitly calculate the fractional powers of wave operators in terms of the fractional Laplacian in bounded smooth domains and characterize the spectrum of these operators.Exploring the gender gap in a closed market niche. Explicit solutions of an ODE modelhttps://zbmath.org/1500.370502023-01-20T17:58:23.823708Z"Sifuentes, David"https://zbmath.org/authors/?q=ai:sifuentes.david"Téllez, Iván"https://zbmath.org/authors/?q=ai:tellez.ivan"Zazueta, Jorge"https://zbmath.org/authors/?q=ai:zazueta.jorgeThe paper builds on the work by \textit{E. Accinelli} and \textit{J. Zazueta} [Exploring the gender gap in the labor market: A sex-disaggregated view, The Social Science Journal, (2021) \url{https://doi.org/10.1080/03623319.2021.1905398}]
by simplifying the model therein and offering analytical solutions to the system of ordinary differential equations describing the growth of the numbers of males and females employed at the labor market. The model may be interpreted as a two-dimensional version of the logistic growth model where the growth term for the employee population of a given sex is a linear combination of both men and women employed (coefficients of the terms represent hiring biases towards their own sex). The overall logistic growth rate of the total employed population equals one, which is an unnecessary model constraint and may easily be dropped by assuming a constant non-unity growth rate. Analytical results for the total employment (in Section 3) follow directly from the logistic growth model and might have been introduced without elaborating own proof.
The added value of the work lies in the analytical solution of the model that also allows offering an analytical expression for the gender gap in employment. Based on the proposed expressions, the authors investigate conditions for the gender gap to close asymptotically (``equality'' condition (15)). However, their main result (Theorem 5.3) is not technically correct, as there exist indefinite number of paths towards equality. The uniqueness of such solutions may only be established in the sense that any solution curve leading to equality must cross similar combination of levels of men and women employed, as established in Theorem 5.2, at some point in time. That point in time, however, is arbitrary; hence, an indefinite number of solution curves satisfy the equality condition. Technically, the problem appears in the last line of the proof to Theorem 5.3. The misfortunate formulation of the Theorem 5.3, however, does not undermine the substantive conclusion: only a specific set of initial conditions may lead to equality under any given set of model parameters. In other words, with model parameters and initial conditions set arbitrarily, the model is unlikely to lead to equality at the labor market.
Here, we come to another limitation of the model regarding its relevance to real-life employment processes. In reality, the employment sectors go through numerous growth and shrinkage phases and those processes involve stochasticity. That might completely change the view to equality implications of the model parameters. Assuming, for example, indefinite number of economic swings and that laying off the labor market happens independently of the sex, one may note that long-term composition of the market will be determined by the first multipliers in Equation (1) and not by the logistic constraint terms. On the other hand, the authors might have deepened their analysis by allowing for `overemployment' solutions with \(f+m<k\), i.e., describing the labor shrinking phases within their own model. This is a missing part of the work that may be considered in a future work.
As a side note, it is worth pointing to possible usefulness of the model proposed in the paper beyond modeling the employment dynamics. One may, for example, consider a logistic model for a population composed of two or more traits that may reproduce one another through mutations.
Reviewer: Dalkhat M. Ediev (Cherkessk)Existence of multiple solutions to a discrete fourth order periodic boundary value problem via variational methodhttps://zbmath.org/1500.390052023-01-20T17:58:23.823708Z"Dhar, Sougata"https://zbmath.org/authors/?q=ai:dhar.sougata"Kong, Lingju"https://zbmath.org/authors/?q=ai:kong.lingjuSummary: By using variational methods and critical point theory, we obtain criteria for the existence of at least three solutions for a generalized fourth order nonlinear difference equation together with periodic boundary conditions. Various special cases of the above problem are discussed. An example is included to illustrate the results.New existence criterion of infinitely many solutions for partial discrete Dirichlet problemshttps://zbmath.org/1500.390062023-01-20T17:58:23.823708Z"Gharehgazlouei, Fariba"https://zbmath.org/authors/?q=ai:gharehgazlouei.fariba"Heidarkhani, Shapour"https://zbmath.org/authors/?q=ai:heidarkhani.shapourSummary: In this paper, we present new existence criterion of solutions for partial discrete Dirichlet problems. More precisely, under appropriate assumptions on the nonlinearities that possesses the appropriate behaviors related to the eigenvalues at infinity, the existence result of infinitely many solutions is discussed.Boundary-value problems for differential-difference equations with incommensurable shifts of arguments reducible to nonlocal problemshttps://zbmath.org/1500.390072023-01-20T17:58:23.823708Z"Ivanova, E. P."https://zbmath.org/authors/?q=ai:ivanova.elena-pavlovnaSummary: We consider boundary-value problems for differential-difference equations containing incommensurable shifts of arguments in higher-order terms. We prove that in the case of finite orbits of boundary points generated by the set of shifts of the difference operator, the original problem is reduced to a boundary-value problem for differential equation with nonlocal boundary conditions.Relations between spectrum curves of discrete Sturm-Liouville problem with nonlocal boundary conditions and graph theoryhttps://zbmath.org/1500.390082023-01-20T17:58:23.823708Z"Vitkauskas, Jonas"https://zbmath.org/authors/?q=ai:vitkauskas.jonas"Štikonas, Artūras"https://zbmath.org/authors/?q=ai:stikonas.arturas(no abstract)Relations between spectrum curves of discrete Sturm-Liouville problem with nonlocal boundary conditions and graph theory. IIhttps://zbmath.org/1500.390092023-01-20T17:58:23.823708Z"Vitkauskas, Jonas"https://zbmath.org/authors/?q=ai:vitkauskas.jonas"Štikonas, Artūras"https://zbmath.org/authors/?q=ai:stikonas.arturas(no abstract)Convergence of perturbation series for unbounded monotone quasiperiodic operatorshttps://zbmath.org/1500.390142023-01-20T17:58:23.823708Z"Kachkovskiy, Ilya"https://zbmath.org/authors/?q=ai:kachkovskiy.ilya-v"Parnovski, Leonid"https://zbmath.org/authors/?q=ai:parnovski.leonid"Shterenberg, Roman"https://zbmath.org/authors/?q=ai:shterenberg.roman-gSummary: We consider a class of unbounded quasiperiodic Schrödinger-type operators on \(\ell^2( \mathbb{Z}^d)\) with monotone potentials (akin to the Maryland model) and show that the Rayleigh-Schrödinger perturbation series for these operators converges in the regime of small kinetic energies, uniformly in the spectrum. As a consequence, we obtain a new proof of Anderson localization in a more general than before class of such operators, with explicit convergent series expansions for eigenvalues and eigenvectors. This result can be restricted to an energy window if the potential is only locally monotone and one-to-one. A modification of this approach also allows the potential to be non-strictly monotone and have a flat segment, under additional restrictions on the frequencies.Spectral analysis of perturbed Fredholm operatorshttps://zbmath.org/1500.470192023-01-20T17:58:23.823708Z"Bouzidi, Sana"https://zbmath.org/authors/?q=ai:bouzidi.sana"Moalla, Nedra"https://zbmath.org/authors/?q=ai:moalla.nedra"Walha, Ines"https://zbmath.org/authors/?q=ai:walha.inesSummary: In this paper, we use a newly introduced perturbation concept in the literature originated by \textit{M. Mbekhta} [J. Oper. Theory 51, No. 1, 3--18 (2004; Zbl 1104.47015)], which is the \(\Phi\)-perturbation function, allowing to derive an original stability results intervening in the theory of perturbed Fredholm operators. Our results are subsequently used to investigate a new characterization of Weyl spectrum of linear operator under such concept of \(\Phi\)-perturbation function. The last part is devoted to study the problem of the stability of perturbed semi-Fredholm operators via this kind of function approach. The theoretical results are illustrated by some examples.Scattering and characteristic functions of a dissipative operator generated by a system of equationshttps://zbmath.org/1500.470512023-01-20T17:58:23.823708Z"Bayram, Elgiz"https://zbmath.org/authors/?q=ai:bayram.elgiz"Taş, Kenan"https://zbmath.org/authors/?q=ai:tas.kenan"Uğurlu, Ekin"https://zbmath.org/authors/?q=ai:ugurlu.ekinSummary: In this paper, we consider a system of first-order equations with the same eigenvalue parameter together with dissipative boundary conditions. Applying Lax-Phillips scattering theory and Sz.-Nagy-Foiaş model operator theory, we prove a completeness theorem.Uniformly exponential dichotomy for strongly continuous quasi groupshttps://zbmath.org/1500.470632023-01-20T17:58:23.823708Z"Sutrima, Sutrima"https://zbmath.org/authors/?q=ai:sutrima.sutrima"Mardiyana, Mardiyana"https://zbmath.org/authors/?q=ai:mardiyana.mardiyana"Setiyowati, Ririn"https://zbmath.org/authors/?q=ai:setiyowati.ririnSufficient and necessary conditions for the uniformly exponential dichotomy of the $C^0$-quasi groups and the $C^0$-quasi semigroups are characterized by the associated evolution semigroups in the paper. The concept $C^0$-quasi semigroup is an alternative tool to discuss non-autonomous equations. $C^0$-quasi semigroups are investigated for spectra and stabilities and applied to controllability, observability, stability, and stabilizability of the non-autonomous linear control systems.
Reviewer: Weinian Zhang (Chengdu)A new proof of Jörgens's resulthttps://zbmath.org/1500.470642023-01-20T17:58:23.823708Z"Shao, Chen"https://zbmath.org/authors/?q=ai:shao.chen"Xu, Gen Qi"https://zbmath.org/authors/?q=ai:xu.gen-qi(no abstract)On traces and modified Fredholm determinants for half-line Schrödinger operators with purely discrete spectrahttps://zbmath.org/1500.470672023-01-20T17:58:23.823708Z"Gesztesy, Fritz"https://zbmath.org/authors/?q=ai:gesztesy.fritz"Kirsten, Klaus"https://zbmath.org/authors/?q=ai:kirsten.klausSummary: After recalling a fundamental identity relating traces and modified Fredholm determinants, we apply it to a class of half-line Schrödinger operators \( (- d^2/dx^2) + q\) on \( (0,\infty )\) with purely discrete spectra. Roughly speaking, the class considered is generated by potentials \( q\) that, for some fixed \( C_0 > 0\), \( \varepsilon > 0\), \( x_0 \in (0, \infty )\), diverge at infinity in the manner that \( q(x) \geq C_0 x^{(2/3) + \varepsilon _0}\) for all \( x \geq x_0\). We treat all self-adjoint boundary conditions at the left endpoint 0.Perturbation theory of maximal monotone operators and its application to differential equationshttps://zbmath.org/1500.470732023-01-20T17:58:23.823708Z"Wei, Li"https://zbmath.org/authors/?q=ai:wei.li(no abstract)On new classes of cyclic (noncyclic) condensing operators with applicationshttps://zbmath.org/1500.470742023-01-20T17:58:23.823708Z"Patle, Pradip Ramesh"https://zbmath.org/authors/?q=ai:patle.pradip-ramesh"Gabeleh, Moosa"https://zbmath.org/authors/?q=ai:gabeleh.moosa"Rakocevic, Vladimir"https://zbmath.org/authors/?q=ai:rakocevic.vladimirSummary: Primarily this work considers the concept of cyclic (noncyclic) Krasnoselskii and Dugundji-Granas condensing operators in Banach spaces. The best proximity point (pair) results are established using the concept of measure of noncompactness for the said operators. An application is presented to show the existence of optimal solutions of a system of Hilfer fractional differential equations with initial conditions.Fixed point theorems for some classes of increasing operators and their applicationshttps://zbmath.org/1500.470782023-01-20T17:58:23.823708Z"Li, Chun Ping"https://zbmath.org/authors/?q=ai:li.chunping"Tian, Qing"https://zbmath.org/authors/?q=ai:tian.qing(no abstract)Solutions of a set-valued mapping equation and their applicationshttps://zbmath.org/1500.470862023-01-20T17:58:23.823708Z"Wu, Yue Xiang"https://zbmath.org/authors/?q=ai:wu.yuexiang"Guo, Chun Mei"https://zbmath.org/authors/?q=ai:guo.chunmei"Huo, Yan Mei"https://zbmath.org/authors/?q=ai:huo.yanmei(no abstract)Nonlocal fractional differential inclusions with impulses at variable timeshttps://zbmath.org/1500.471252023-01-20T17:58:23.823708Z"Ouahab, A."https://zbmath.org/authors/?q=ai:ouahab.abdelghani"Seghiri, S."https://zbmath.org/authors/?q=ai:seghiri.sBy utilizing the measure of noncompactness, multivalued fixed point theory, and fractional calculus, the authors obtain the existence of mild solutions for a fractional semilinear differential inclusions with nonlocal conditions and impulses at variable times. Moreover, the topological properties of the solution set are investigated. Some known results are extended.
Reviewer: Chuanzhi Bai (Huaian)Delaunay surfaces of prescribed mean curvature in \(\mathrm{Nil}_3\) and \(\widetilde{SL_2}(\mathbb{R})\)https://zbmath.org/1500.530742023-01-20T17:58:23.823708Z"Bueno, Antonio"https://zbmath.org/authors/?q=ai:bueno.antonioSummary: We obtain a classification result for rotational surfaces in the Heisenberg space and the universal cover of the special linear group, whose mean curvature is given as a prescribed \(C^1\) function depending on their angle function. We show that these surfaces behave like the Delaunay surfaces of constant mean curvature, under some assumptions on the prescribed function. In contrast with the constant mean curvature case, we exhibit the existence of rotational, embedded tori, providing counterexamples of the Alexandrov problem for this class of immersed surfaces.On exponential stability of non-autonomous stochastic differential equations with Markovian switchinghttps://zbmath.org/1500.600342023-01-20T17:58:23.823708Z"Tran, Ky Q."https://zbmath.org/authors/?q=ai:tran.ky-quan"Le, Bich T. N."https://zbmath.org/authors/?q=ai:le.bich-t-nSummary: This paper is devoted to exponential stability of a class of non-autonomous stochastic differential equations with Markovian switching. By making use the time inhomogeneous property of the drift and diffusion coefficients, we derive sufficient and verifiable conditions for moment exponential stability and almost sure exponential stability. The contribution of the Markovian switching and time-inhomogeneous property to the stability is revealed. Two examples are provided to illustrate the effectiveness of our criteria.Constant step stochastic approximations involving differential inclusions: stability, long-run convergence and applicationshttps://zbmath.org/1500.600402023-01-20T17:58:23.823708Z"Bianchi, Pascal"https://zbmath.org/authors/?q=ai:bianchi.pascal"Hachem, Walid"https://zbmath.org/authors/?q=ai:hachem.walid"Salim, Adil"https://zbmath.org/authors/?q=ai:salim.adilSummary: We consider a Markov chain \((x_n)\) whose kernel is indexed by a scaling parameter \(\gamma > 0\), referred to as the step size. The aim is to analyze the behaviour of the Markov chain in the doubly asymptotic regime where \(n \to \infty\) then \(\gamma \to \infty\). First, under mild assumptions on the so-called drift of the Markov chain, we show that the interpolated process converges narrowly to the solutions of a Differential Inclusion (DI) involving an upper semicontinuous set-valued map with closed and convex values. Second, we provide verifiable conditions which ensure the stability of the iterates. Third, by putting the above results together, we establish the long run convergence of the iterates as \(\gamma \to \infty\), to the Birkhoff center of the DI. The ergodic behaviour of the iterates is also provided. Application examples are investigated. We apply our findings to (1) the problem of nonconvex proximal stochastic optimization and (2) a fluid model of parallel queues.A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivativehttps://zbmath.org/1500.650242023-01-20T17:58:23.823708Z"Heydari, M. H."https://zbmath.org/authors/?q=ai:heydari.mohammad-hossien"Razzaghi, M."https://zbmath.org/authors/?q=ai:razzaghi.mohsenSummary: In this study, a kind of piecewise fractional derivatives based on the Caputo fractional derivative is used to define a novel category of fractional optimal control problems. The piecewise Chebyshev cardinal functions as an appropriate family of basis functions are considered to construct a numerical method for solving such problems. The classical and piecewise fractional derivative matrices of these basis functions are derived and used in constructing the proposed technique. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The accuracy of the expressed approach is investigated by solving some examples.Understanding the acceleration phenomenon via high-resolution differential equationshttps://zbmath.org/1500.650262023-01-20T17:58:23.823708Z"Shi, Bin"https://zbmath.org/authors/?q=ai:shi.bin"Du, Simon S."https://zbmath.org/authors/?q=ai:du.simon-s"Jordan, Michael I."https://zbmath.org/authors/?q=ai:jordan.michael-irwin"Su, Weijie J."https://zbmath.org/authors/?q=ai:su.weijie-jSummary: Gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distinguish between two fundamentally different algorithms -- Nesterov's accelerated gradient method for strongly convex functions (NAG-SC) and Polyak's heavy-ball method -- we study an alternative limiting process that yields \textit{high-resolution ODEs}. We show that these ODEs permit a general Lyapunov function framework for the analysis of convergence in both continuous and discrete time. We also show that these ODEs are more accurate surrogates for the underlying algorithms; in particular, they not only distinguish between NAG-SC and Polyak's heavy-ball method, but they allow the identification of a term that we refer to as ``gradient correction'' that is present in NAG-SC but not in the heavy-ball method and is responsible for the qualitative difference in convergence of the two methods. We also use the high-resolution ODE framework to study Nesterov's accelerated gradient method for (non-strongly) convex functions, uncovering a hitherto unknown result -- that NAG-C minimizes the squared gradient norm at an inverse cubic rate. Finally, by modifying the high-resolution ODE of NAG-C, we obtain a family of new optimization methods that are shown to maintain the accelerated convergence rates of NAG-C for smooth convex functions.Numerical study on fractional-order Lotka-Volterra model with spectral method and Adams-Bashforth-Moulton methodhttps://zbmath.org/1500.651072023-01-20T17:58:23.823708Z"Ghosh, Surath"https://zbmath.org/authors/?q=ai:ghosh.surathSummary: In this work, a corelative study is described to solve Lotka-Volterra (LV) model which is an important model in biological science. In this study, the LV equations are solved by spectral method (SM) with shifted Chebyshev polynomials of first kind and Adams-Bashforth-Moulton predictor corrector method (ABM). Here, we obtain a system of non-linear algebraic equations using SM. Then these kind of system of equations are solved using matlab. Also the solutions are compared with the ABM method. The time for computation for getting the solutions is so less. So, cost is minimum. Two different cases of solution are described to obtain accurate and efficient results.Immune response model fitting to \(\mathrm{CD4^+}\) \(\mathrm{T}\) cell data in \textit{lymphocytic choriomeningitis virus} LCMV infectionhttps://zbmath.org/1500.920182023-01-20T17:58:23.823708Z"Afsar, Atefeh"https://zbmath.org/authors/?q=ai:afsar.atefeh"Martins, Filipe"https://zbmath.org/authors/?q=ai:martins.filipe"Oliveira, Bruno M. P. M."https://zbmath.org/authors/?q=ai:oliveira.bruno-m-p-m"Pinto, Alberto A."https://zbmath.org/authors/?q=ai:pinto.alberto-adregoSummary: We make two fits of an ODE system with 5 equations that model immune response by \(\mathrm{CD4^+}\) \(\mathrm{T}\) cells with the presence of regulatory T cells (Tregs). We fit the simulations to data regarding gp61 and NP309 epitopes from mice infected with \textit{lymphocytic choriomeningitis virus} LCMV. We optimized parameters relating to: the T cell maximum growth rate; the T cell capacity; the T cell homeostatic level; and the ending time of the immune activation phase after infection. We quantitatively and qualitatively compare the obtained results with previous fits in the literature using different ODE models and we show that we are able to calibrate the model and obtain good fits describing the data.
For the entire collection see [Zbl 1481.92004].Mathematical analysis of a model for chronic myeloid leukemiahttps://zbmath.org/1500.920192023-01-20T17:58:23.823708Z"Derrar, Fatima Zohra Elouchdi"https://zbmath.org/authors/?q=ai:derrar.fatima-zohra-elouchdi"Benmerzouk, Djamila"https://zbmath.org/authors/?q=ai:benmerzouk.djamila"Ainseba, Bedr'Eddine"https://zbmath.org/authors/?q=ai:ainseba.bedreddineSummary: In this paper, a mathematical analysis of a model describing the evolution of chronic myeloid leukemic with effect of growth factors is considered. The corresponding dynamics are represented by a system of ordinary differential equations of dimension 5. This system described the interactions between hematopoietic stem cells (HSC), hematopoietic mature cells (MC), cancer hematopoietic stem cells, cancer hematopoietic mature cells and the associated growth factor concentration. Our research is, henceforth, carried out on the existence and the uniqueness of the solution of this system. The next substantive concern will be a discussion on the local and global stability of the corresponding steady states. Three scenarios, however, corresponding to different actions of hematopoiesis on stem cells (differentiate cells or both cells) are considered.Bifurcation analysis of a tumour-immune model with nonlinear killing rate as state-dependent feedback controlhttps://zbmath.org/1500.920212023-01-20T17:58:23.823708Z"Guan, Likun"https://zbmath.org/authors/?q=ai:guan.likun"Yang, Jin"https://zbmath.org/authors/?q=ai:yang.jin"Tan, Yuanshun"https://zbmath.org/authors/?q=ai:tan.yuanshun"Liu, Zijian"https://zbmath.org/authors/?q=ai:liu.zijian"Cheke, Robert A."https://zbmath.org/authors/?q=ai:cheke.robert-aSummary: Impulsive control strategies have been widely used in cancer treatment and linear impulsive control has always been considered in previous studies. We propose a novel tumour-immune model with nonlinear killing rate as state-dependent feedback control, which can better reflect the saturation effects of the tumour and immune cell mortalities due to chemotherapy, and its dynamic behaviors are investigated. The paper aims to discuss the transcritical and subcritical bifurcations of the model. To begin with, the threshold conditions for tumour eradication and tumour persistence in the model without pulse interventions are provided. We define the Poincaré map of the proposed model and then address the existence and orbital asymptotically stability of the model's tumour-free periodic solution. Furthermore, by using the bifurcation theory of the discrete one-parameter family of maps, which is determined by the Poincaré mapping, we investigate the model's transcritical and subcritical pitchfork bifurcations with respect to the key parameter.Complex dynamic behaviors of a tumor-immune system with two delays in tumor actionshttps://zbmath.org/1500.920222023-01-20T17:58:23.823708Z"Li, Jianquan"https://zbmath.org/authors/?q=ai:li.jianquan"Ma, Xiangxiang"https://zbmath.org/authors/?q=ai:ma.xiangxiang"Chen, Yuming"https://zbmath.org/authors/?q=ai:chen.yuming"Zhang, Dian"https://zbmath.org/authors/?q=ai:zhang.dianSummary: The action of a tumor on the immune system includes stimulation and neutralization, which usually have different time delays. In this work we propose a tumor-immune system to incorporate these two kinds of delays due to tumor actions. We explore effects of time delays on the model and find some different phenomena induced by them. When there is only the neutralization delay, the model has a uniform upper bound while when there is only the stimulation delay, the bound varies with the delay. The theoretic analysis suggests that, for the model only with the stimulation delay, the stability of its tumor-present equilibrium may change at most once as the delay increases, but the increase of the neutralization delay may lead to multiple stability switches for the model only with the neutralization delay. Numerical simulations indicate that, in the presence of the neutralization delay, the stimulation delay may induce multiple stability switches. Further, when the model has two tumor-present equilibria, numerical simulations also demonstrate that the model may present some interesting outcomes as each of the two delays increases. These phenomena include the onset of the cytokine storm, the almost global attractivity of the tumor-free equilibrium for sufficiently large time delays, and so on. These results show the complexity of the dynamic behaviors of the model and different effects of the two time delays.Bifurcations and bistability of an age-structured viral infection model with a nonmonotonic immune responsehttps://zbmath.org/1500.920242023-01-20T17:58:23.823708Z"Wang, Shaoli"https://zbmath.org/authors/?q=ai:wang.shaoli"Wang, Tengfei"https://zbmath.org/authors/?q=ai:wang.tengfei"Chen, Yuming"https://zbmath.org/authors/?q=ai:chen.yuming|chen.yuming.1Summary: Recent studies have demonstrated that immune impairment is an essential factor in viral infection for disease development and treatment. In this paper, we formulate an age-structured viral infection model with a nonmonotonic immune response and perform dynamical analysis to explore the effects of both immune impairment and virus control. The basic infection reproduction number is derived for a general viral production rate, which determines the global stability of the infection-free equilibrium. For the immune intensity, we get two important thresholds, the post-treatment control threshold and the elite control threshold. The interval between the two thresholds is a bistable interval, where there are two immune-present infected equilibria. When the immune intensity is greater than the elite control threshold, only one immune-present infected equilibrium exists and it is stable. By assuming the death rate and virus production rate of infected cells to be constants, with the immune intensity as a bifurcation parameter, the system exhibits saddle-node bifurcation, transcritical bifurcation, and backward/forward bifurcation.Noise-induced multirhythmicity, bursting, and order-chaos transitions in the 3D Goldbeter systemhttps://zbmath.org/1500.920292023-01-20T17:58:23.823708Z"Ryashko, Lev"https://zbmath.org/authors/?q=ai:ryashko.lev-borisovichSummary: Motivated by an attractive problem of elucidating the causes for the occurrence of complex oscillatory regimes in chemical reactions, we study the constructive role of noise in a three-dimensional enzymatic ``substrate-two products'' model. Stochastic effects are investigated in the parameter zone of birhythmicity where regular oscillatory attractors coexist with chaotic ones. Chaos-order transformations caused by stochastic transitions between these attractors are studied parametrically using the Lyapunov exponents. A special form of stochastic excitement of large-amplitude bursts consisting of the high-frequency spikes is revealed and investigated by statistical analysis.Stochastic P-bifurcation in a delayed Myc/E2F/miR-17-92 networkhttps://zbmath.org/1500.920332023-01-20T17:58:23.823708Z"Han, Zikun"https://zbmath.org/authors/?q=ai:han.zikun"Wang, Qiubao"https://zbmath.org/authors/?q=ai:wang.qiubao"Wu, Hao"https://zbmath.org/authors/?q=ai:wu.hao.7|wu.hao.3|wu.hao.2|wu.hao.6|wu.hao|wu.hao.1|wu.hao.5"Hu, Zhouyu"https://zbmath.org/authors/?q=ai:hu.zhouyuSummary: In this paper, Myc/E2F/miR-17-92 network under Gaussian white noise is studied. Taking the time delay as the parameter, the Hopf bifurcation of the system is obtained, which causes the protein concentration to oscillate periodically. Under the influence of time delay and noise, the stochastic D-bifurcation of the system is obtained. It is worth noting that the occurrence of stochastic P-bifurcation is successfully captured. Thus a pattern of coexistence of high and low protein concentrations is founded in the network. The specific research methods of this paper are as follows: firstly, the system is reduced to a finite dimensional system by using stochastic center manifold and normal form theory. Then, using the stochastic averaging method, the Fokker-Planck-Kolmogorov equation of the system is constructed in which the statistical response in the stationary state is the probability density. Finally, the stochastic bifurcation analysis and numerical simulation are carried out. The agreements between the analytical method and those obtained numerically validate the effectiveness of the analytical investigations.Stability analysis, Hopf bifurcation and drug therapy control of an HIV viral infection model with logistic growth rate and cell-to-cell and cell-free transmissionshttps://zbmath.org/1500.920512023-01-20T17:58:23.823708Z"Roomi, Vahid"https://zbmath.org/authors/?q=ai:roomi.vahid"Gharahasanlou, Tohid Kasbi"https://zbmath.org/authors/?q=ai:gharahasanlou.tohid-kasbi"Hemmatzadeh, Zeynab"https://zbmath.org/authors/?q=ai:hemmatzadeh.zeynabSummary: It is well known that dynamical systems are very useful tools to study viral diseases such as HIV, HBV, HCV, Ebola and influenza. This paper focuses on a mathematical model of the cell-to-cell and the cell-free spread of HIV with both linear and nonlinear functional responses and logistic target cell growth. The reproduction number of each mode of transmission has been calculated and their sum has been considered as the basic reproduction number. Based on the values of the reproduction number, the local and global stabilities of the rest points are investigated. Choosing a suitable bifurcation parameter, some conditions for the occurrence of Hopf bifurcation are also obtained. Moreover, numerical simulations are presented to support the analytical results. Finally, to study the effect of the drug on the disease process, some control conditions are determined. Since two modes of transmission and both linear and nonlinear functional responses have been included in this manuscript, our obtained results are a generalization of those in the literature. Moreover, the results are obtained with weaker assumptions in comparison with the previous ones.Effects of predator-driven prey dispersal on sustainable harvesting yieldhttps://zbmath.org/1500.920862023-01-20T17:58:23.823708Z"Bhattacharyya, Joydeb"https://zbmath.org/authors/?q=ai:bhattacharyya.joydeb"Piiroinen, Petri T."https://zbmath.org/authors/?q=ai:piiroinen.petri-t"Banerjee, Soumitro"https://zbmath.org/authors/?q=ai:banerjee.soumitroSummary: Dispersal of organisms between patches is a common phenomenon in ecology and plays an important role in predator-prey population dynamics. We propose a nonsmooth Filippov predator-prey model in a two-patch environment characterized by a generalist predator-driven intermittent refuge protection of an apprehensive prey along with a balanced dispersal of the prey between refuge and nonrefuge areas. By employing qualitative techniques of nonsmooth dynamical systems, we see that the switching surface is a repeller whenever the interior equilibria are virtual, causing long-term population fluctuations. We find that the level of prey vigilance and the rate of prey dispersal play pivotal roles in the total harvesting yield. We observe that a sustainable high harvesting yield is possible when the prey is less vigilant and obtain the harvesting efforts for maximum sustainable total yield (MSTY). We further modify the model by considering a continuous threshold predator-driven prey dispersal and show that the model exhibits a Hopf bifurcation when the level of prey vigilance exceeds some critical threshold value. By comparing the dynamics of the two models we see that for a sustainable high harvesting yield of the system with continuous threshold dispersal, the prey needs to be highly vigilant compared to that of the system with intermittent dispersal of the prey. Further, we find numerically that the estimated MSTY from both models remains the same.Complex dynamics on a discrete tritrophic model of Leslie type with general functional responseshttps://zbmath.org/1500.920872023-01-20T17:58:23.823708Z"Blé, Gamaliel"https://zbmath.org/authors/?q=ai:ble.gamaliel"Dela-Rosa, Miguel Angel"https://zbmath.org/authors/?q=ai:dela-rosa.miguel-angelSummary: In this paper, by averaging the growth rate on each state, we analyze the dynamics of a discrete dynamical system coming from a system of ODEs. This differential system corresponds to a tritrophic Leslie type model which is formed by three populations (prey (P), mesopredator (MP) and superpredator (SP)), where the last two populations are generalist predators. We give sufficient conditions where the discrete model undergoes a Neimark-Sacker bifurcation at a coexistence point. This analysis is independent of the functional responses that govern the interactions. To illustrate our results, several applications are given, under the assumptions that the population P has logistic growth and that the relations MP-P and SP-MP are carried out through Holling type functional responses. From these applications, we conclude that there are sufficient conditions to guarantee that the three species coexist by means of a supercritical Neimark-Sacker bifurcation. Moreover, numerically we can detect that the discrete system exhibits a chaotic behavior.Reduced oviposition period promotes blowfly population extinction in Nicholson's modelhttps://zbmath.org/1500.920902023-01-20T17:58:23.823708Z"Elbaz, Islam M."https://zbmath.org/authors/?q=ai:elbaz.islam-mSummary: Blowflies use open wounds or the accumulation of feces or urine in wool to lay their eggs. The larvae that emerge cause lesions in the host sheep, which can lead to death. They are found in Australia, New Zealand, and the United Kingdom. Nicholson's model describes the population dynamics of the Australian blowfly (\textit{Lucilia cuprina}). It incorporates environmental variation. The extinction of these flies depends on the time to oviposition and the time between generations. The Lyapunov function, which is positive with a negative derivative, provides the condition for the stability of the equilibrium point: the oviposition period must be sufficiently short, because the shorter it is, the more it favors the extinction of the species. The zero solution is the only equilibrium point, synonymous with the extinction of the population. Another species of blowfly, \textit{Lucilia sericata}, also attacks sheep in Australia. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to share same mitochondrial DNA sequences, although the two species are distinct. Presumably to avoid competition between them. the egg-laying time of each species does not occur at the same time of year: \textit{L. sericata} prefers warmer months, thus in summer, while \textit{L. cuprina} is mainly active in autumn. Laying of eggs in different months allows avoiding competition between these species. This also binds them together. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations, provided they do not adapt.Predator-prey system with multiple delays: prey's countermeasures against juvenile predators in the predator-prey conflicthttps://zbmath.org/1500.920912023-01-20T17:58:23.823708Z"Kaushik, Rajat"https://zbmath.org/authors/?q=ai:kaushik.rajat"Banerjee, Sandip"https://zbmath.org/authors/?q=ai:banerjee.sandip(no abstract)Analysis of the onset of a regime shift and detecting early warning signs of major population changes in a two-trophic three-species predator-prey model with long-term transientshttps://zbmath.org/1500.920942023-01-20T17:58:23.823708Z"Sadhu, Susmita"https://zbmath.org/authors/?q=ai:sadhu.susmitaSummary: Identifying early warning signs of sudden population changes and mechanisms leading to regime shifts are highly desirable in population biology. In this paper, a two-trophic ecosystem comprising of two species of predators, competing for their common prey, with explicit interference competition is considered. With proper rescaling, the model is portrayed as a singularly perturbed system with fast prey dynamics and slow dynamics of the predators. In a parameter regime near singular Hopf bifurcation, chaotic mixed-mode oscillations (MMOs), featuring concatenation of small and large amplitude oscillations are observed as long-lasting transients before the system approaches its asymptotic state. To analyze the dynamical cause that initiates a large amplitude oscillation in an MMO orbit, the model is reduced to a suitable normal form near the singular-Hopf point. The normal form possesses a separatrix surface that separates two different types of oscillations. A large amplitude oscillation is initiated if a trajectory moves from the ``inner'' to the ``outer side'' of this surface. A set of conditions on the normal form variables are obtained to determine whether a trajectory would exhibit another cycle of MMO dynamics before experiencing a regime shift (i.e. approaching its asymptotic state). These conditions serve as early warning signs for a sudden population shift as well as detect the onset of a regime shift in this ecological model.Stability and bifurcation in a prey-predator-scavenger system with Michaelis-Menten type of harvesting functionhttps://zbmath.org/1500.920952023-01-20T17:58:23.823708Z"Satar, Huda Abdul"https://zbmath.org/authors/?q=ai:abdul-satar.huda"Naji, Raid Kamel"https://zbmath.org/authors/?q=ai:naji.raid-kamelSummary: In this paper an ecological model consisting of prey-predator-scavenger involving Michaelis-Menten type of harvesting function is proposed and studied. The existence, uniqueness and uniformly bounded of the solution of the proposed model are discussed. The stability and persistence conditions of the model are established. Lyapunov functions are used to study the global stability of all equilibrium points. The possibility of occurrence of local bifurcation around the equilibrium points is investigated. Finally an extensive numerical simulation is carried out to validate the obtained analytical results and understand the effects of scavenger and harvesting on the model dynamics. It is observed that the proposed model is very sensitive for varying in their parameters values especially those related with scavenger and undergoes different types of local bifurcation.Bifurcations and chaos control in a discrete-time prey-predator model with Holling type-II functional response and prey refugehttps://zbmath.org/1500.920962023-01-20T17:58:23.823708Z"Singh, Anuraj"https://zbmath.org/authors/?q=ai:singh.anuraj"Sharma, Vijay Shankar"https://zbmath.org/authors/?q=ai:sharma.vijay-shankarSummary: In this paper, we study the complex dynamical behavior in a discrete prey-predator model with Holling type II functional response with prey refuge. It is exhibited that the system shows different types of bifurcations viz. flip bifurcation, transcritical bifurcation and Neimark-Sacker bifurcation (NSB) by using center manifold theorem and bifurcation theory. Moreover, the chaos occurred in the system has been controlled by deploying control strategies viz. state feedback, pole placement and hybrid control techniques. The certain conditions have been determined under which chaos and bifurcation can be stabilized. The extensive numerical simulation is performed to demonstrate the analytical findings.Population dynamic consequences of fearful prey in a spatiotemporal predator-prey systemhttps://zbmath.org/1500.920972023-01-20T17:58:23.823708Z"Upadhyay, Ranjit Kumar"https://zbmath.org/authors/?q=ai:kumar-upadhyay.ranjit"Mishra, Swati"https://zbmath.org/authors/?q=ai:mishra.swatiThe authors formulate a spatial predator-prey model considering the effect of fear which evokes various different responses concerning the physiology, morphology, ontogeny and the behavior of scared organisms. In this work, the authors incorporate this phenomenon in their Leslie-Gower type predator-prey model model by introducing the cost of fear in the prey reproduction term. The main focus is on studying the influence of anti-predator behaviours due to fear of predators in both space and time. The global dynamics of the temporal model is described first. Then Turing instability, the existence of Hopf bifurcation, direction and stability of bifurcating periodic solutions are determined for the spatially explicit model system. Conditions for Turing pattern formation are obtained through diffusion-driven instability. Numerical experiments are provided for both the temporal and the spatiotemporal model system, several Turing patterns are presented suggesting that the change in the level of fear and diffusion coefficients alter these structures significantly. The authors find that the increase in fear level can decrease the population size of both species.
Reviewer: Attila Dénes (Szeged)Exponential extinction of a stochastic predator-prey model with Allee effecthttps://zbmath.org/1500.920992023-01-20T17:58:23.823708Z"Zhang, Beibei"https://zbmath.org/authors/?q=ai:zhang.beibei"Wang, Hangying"https://zbmath.org/authors/?q=ai:wang.hangying"Lv, Guangying"https://zbmath.org/authors/?q=ai:lv.guangyingIn population dynamics, the Allee effect refers to a positive density dependence in prey population growth at small prey population sizes. Predator-prey model with Allee effect can describe more complex phenomenon. In this paper, the authors study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, whose coefficients are dependent on expectations. The authors prove that there is a unique global positive solution to the system with the positive initial value. Moreover, sufficient conditions for exponential extinction are established. The main reference is the works of \textit{B. Tian} et al. [Int. J. Biomath. 8, No. 4, Article ID 1550044, 15 p. (2015; Zbl 1328.92070)].
Reviewer: Yingxin Guo (Qufu)Mathematical modelling of cockroach involvement in foodborne disease transmission in human habitathttps://zbmath.org/1500.921002023-01-20T17:58:23.823708Z"Afassinou, Komi"https://zbmath.org/authors/?q=ai:afassinou.komiSummary: Cockroaches are among the most common pests in many houses and other food processing areas. Their co-habitation with humans have raised public health concerns and posed serious risks to humans health, as they are suspected to play an important role in the transmission of different intestinal diseases including diarrhoea, dysentery, cholera, leprosy plague and typhoid fever. In this article, we present a mathematical model that depicts foodborne disease transmission to humans by cockroaches to incorporate control interventions such as insecticides use and regular environmental sanitation. The mathematical and numerical analyses are conducted to investigate the impact of these control interventions when considered as a single or combined strategies. The results reveal the efficacy level of the insecticides beyond which a total eradication is possible. Use of baits and trapping devices intervention is also explored and revealed to be the best.Dynamics of a stochastic SIR epidemic model driven by Lévy jumps with saturated incidence rate and saturated treatment functionhttps://zbmath.org/1500.921052023-01-20T17:58:23.823708Z"EL Koufi, Amine"https://zbmath.org/authors/?q=ai:el-koufi.amine"Adnani, Jihad"https://zbmath.org/authors/?q=ai:adnani.jihad"Bennar, Abdelkrim"https://zbmath.org/authors/?q=ai:bennar.abdelkrim"Yousfi, Noura"https://zbmath.org/authors/?q=ai:yousfi.nouraSummary: In this article, we consider a stochastic SIR model with a saturated incidence rate and saturated treatment function incorporating Lévy noise. First, we prove the existence of a unique global positive solution to the model. We investigate the stability of the free equilibria \(E_0\) by using the Lyapunov method. We give sufficient conditions for the persistence in the mean. We show the dynamic properties of the solution around endemic equilibria point of the deterministic model. Moreover, we display some numerical results to confirm our theoretical results.Dynamical analysis of a novel discrete fractional SITRS model for COVID-19https://zbmath.org/1500.921062023-01-20T17:58:23.823708Z"Elsonbaty, Amr"https://zbmath.org/authors/?q=ai:elsonbaty.amr-r"Sabir, Zulqurnain"https://zbmath.org/authors/?q=ai:sabir.zulqurnain"Ramaswamy, Rajagopalan"https://zbmath.org/authors/?q=ai:ramaswamy.rajagopalan"Adel, Waleed"https://zbmath.org/authors/?q=ai:adel.waleedSummary: In this paper, a discrete fractional susceptible-infected-treatment-recovered-susceptible (SITRS) model for simulating the coronavirus (COVID-19) pandemic is presented. The model is a modification to a recent continuous-time SITR model by taking into account the possibility that people who have been infected before can lose their temporary immunity and get reinfected. Moreover, a modification is suggested in the present model to correct the improper assumption that the infection rates of both normal susceptible and old aged/seriously diseased people are equal. This modification complies with experimental data. The equilibrium points for the proposed model are found and results of thorough stability analysis are discussed. A full numerical simulation is carried out and gives a better analysis of the disease spread, influences of model's parameters, and how to control the virus. Comparisons with clinical data are also provided.Strict Lyapunov functions and feedback controls for SIR models with quarantine and vaccinationhttps://zbmath.org/1500.921072023-01-20T17:58:23.823708Z"Ito, Hiroshi"https://zbmath.org/authors/?q=ai:ito.hiroshi|ito.hiroshi-t|ito.hiroshi-c"Malisoff, Michael"https://zbmath.org/authors/?q=ai:malisoff.michael"Mazenc, Frédéric"https://zbmath.org/authors/?q=ai:mazenc.fredericSummary: We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals.Hyper-differential sensitivity analysis for inverse problems governed by ODEs with application to COVID-19 modelinghttps://zbmath.org/1500.921182023-01-20T17:58:23.823708Z"Stevens, Mason"https://zbmath.org/authors/?q=ai:stevens.mason"Sunseri, Isaac"https://zbmath.org/authors/?q=ai:sunseri.isaac"Alexanderian, Alen"https://zbmath.org/authors/?q=ai:alexanderian.alenSummary: We consider inverse problems governed by systems of ordinary differential equations (ODEs) that contain uncertain parameters in addition to the parameters being estimated. In such problems, which are common in applications, it is important to understand the sensitivity of the solution of the inverse problem to the uncertain model parameters. It is also of interest to understand the sensitivity of the inverse problem solution to different types of measurements or parameters describing the experimental setup. Hyper-differential sensitivity analysis (HDSA) is a sensitivity analysis approach that provides tools for such tasks. We extend existing HDSA methods by developing methods for quantifying the uncertainty in the estimated parameters. Specifically, we propose a linear approximation to the solution of the inverse problem that allows efficiently approximating the statistical properties of the estimated parameters. We also explore the use of this linear model for approximate global sensitivity analysis. As a driving application, we consider an inverse problem governed by a COVID-19 model. We present comprehensive computational studies that examine the sensitivity of this inverse problem to several uncertain model parameters and different types of measurement data. Our results also demonstrate the effectiveness of the linear approximation model for uncertainty quantification in inverse problems and for parameter screening.Global stability of a diffusive HCV infections epidemic model with nonlinear incidencehttps://zbmath.org/1500.921202023-01-20T17:58:23.823708Z"Su, Ruyan"https://zbmath.org/authors/?q=ai:su.ruyan"Yang, Wensheng"https://zbmath.org/authors/?q=ai:yang.wensheng(no abstract)Dynamic analysis of a SIQR epidemic model considering the interaction of environmental differenceshttps://zbmath.org/1500.921212023-01-20T17:58:23.823708Z"Wang, Mingjian"https://zbmath.org/authors/?q=ai:wang.mingjian"Hu, Yuhan"https://zbmath.org/authors/?q=ai:hu.yuhan"Wu, Libing"https://zbmath.org/authors/?q=ai:wu.libing(no abstract)Mathematical analysis of a delayed HIV infection model with saturated CTL immune response and immune impairmenthttps://zbmath.org/1500.921232023-01-20T17:58:23.823708Z"Yang, Yan"https://zbmath.org/authors/?q=ai:yang.yan"Xu, Rui"https://zbmath.org/authors/?q=ai:xu.rui.3|xu.rui.1|xu.rui.2|xu.rui(no abstract)A mathematical model of COVID-19 and the multi fears of the community during the epidemiological stagehttps://zbmath.org/1500.921242023-01-20T17:58:23.823708Z"Yousef, Ali"https://zbmath.org/authors/?q=ai:yousef.ali-a|yousef.ali-s"Bozkurt, Fatma"https://zbmath.org/authors/?q=ai:bozkurt.fatma"Abdeljawad, Thabet"https://zbmath.org/authors/?q=ai:abdeljawad.thabet"Emreizeeq, Emad"https://zbmath.org/authors/?q=ai:emreizeeq.emadSummary: Within two years, the world has experienced a pandemic phenomenon that changed almost everything in the macro and micro-environment; the economy, the community's social life, education, and many other fields. Governments started to collaborate with health institutions and the WHO to control the pandemic spread, followed by many regulations such as wearing masks, maintaining social distance, and home office work. While the virus has a high transmission rate and shows many mutated forms, another discussion appeared in the community: the fear of getting infected and the side effects of the produced vaccines.
The community started to face uncertain information spread through some networks keeping the discussions of side effects on-trend. However, this pollution spread confused the community more and activated multi fears related to the virus and the vaccines. This paper establishes a mathematical model of COVID-19, including the community's fear of getting infected and the possible side effects of the vaccines. These fears appeared from uncertain information spread through some social sources. Our primary target is to show the psychological effect on the community during the pandemic stage. The theoretical study contains the existence and uniqueness of the IVP and, after that, the local stability analysis of both equilibrium points, the disease-free and the positive equilibrium point. Finally, we show the global asymptotic stability holds under specific conditions using a suitable Lyapunov function. In the end, we conclude our theoretical findings with some simulations.An epidemic model with transport-related infection incorporating awareness and screeninghttps://zbmath.org/1500.921252023-01-20T17:58:23.823708Z"Zewdie, Assefa Denekew"https://zbmath.org/authors/?q=ai:zewdie.assefa-denekew"Gakkhar, Sunita"https://zbmath.org/authors/?q=ai:gakkhar.sunita(no abstract)A fractional-order food chain system incorporating Holling-II type functional response and prey refugehttps://zbmath.org/1500.921282023-01-20T17:58:23.823708Z"Zhang, Na"https://zbmath.org/authors/?q=ai:zhang.na"Kao, Yonggui"https://zbmath.org/authors/?q=ai:kao.yongguiSummary: A fractional-order three-species food chain ecosystem with prey refuge and Holling-II type functional response for predation is proposed and studied. Several sufficient conditions for the existence and uniqueness of the solution of the fractional-order system are obtained. The boundedness of the solution of the system is proven. We investigate the asymptotic behavior of the model by using eigenvalue analysis, and some sufficient conditions on local asymptotic stability of the equilibrium points are given. Furthermore, the conditions for the occurrence of bifurcation at some equilibrium points are presented. We find that the order of the proposed fractional-order ecosystem is one of the parameters for its bifurcation. Several numerical simulations are provided to show the effectiveness of our findings in this paper. Lastly, some new numerical simulations are given to discuss the influence of the half-saturation constant, prey refuge coefficient and the order of fractional-order derivative on the stability of the discussed fractional-order system.Flocking under hierarchical leadership with symmetrical and asymmetrical delayshttps://zbmath.org/1500.930052023-01-20T17:58:23.823708Z"Wu, Chen"https://zbmath.org/authors/?q=ai:wu.chen"Jin, Yinghua"https://zbmath.org/authors/?q=ai:jin.yinghuaSummary: This paper delves into the flocking behavior of a class of multi-agent systems with symmetrical and asymmetrical delays under hierarchical leadership. First, we present the two corresponding models. Then, mainly using mathematical induction and considering the nature of differential and quadratic functions, we prove that the group can realize flocking with the two types of delays under certain conditions. Finally, we validate the conclusions via numerical simulation results.Approximate controllability of neutral delay integro-differential inclusion of order \(\alpha\in (1, 2)\) with non-instantaneous impulseshttps://zbmath.org/1500.930092023-01-20T17:58:23.823708Z"Kumar, Avadhesh"https://zbmath.org/authors/?q=ai:kumar.avadhesh"Kumar, Ankit"https://zbmath.org/authors/?q=ai:kumar.ankit"Vats, Ramesh Kumar"https://zbmath.org/authors/?q=ai:vats.ramesh-kumar"Kumar, Parveen"https://zbmath.org/authors/?q=ai:kumar.parveenSummary: This paper aims to establish the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay. Sufficient conditions for approximate controllability have been established for the proposed control problem. The tools for study include the fixed point theorem for discontinuous multi-valued operators with the \(\alpha\)-resolvent operator. Finally, the proposed results are illustrated with the help of an example.Controllability of Hilfer fractional Langevin dynamical system with impulse in an abstract weighted spacehttps://zbmath.org/1500.930112023-01-20T17:58:23.823708Z"Radhakrishnan, B."https://zbmath.org/authors/?q=ai:radhakrishnan.bharathkumar|radhakrishnan.bheeman|radhakrishnan.balachandran-g"Sathya, T."https://zbmath.org/authors/?q=ai:sathya.tSummary: The foremost goal of this paper is to study the sufficient conditions for controllability of Hilfer fractional Langevin dynamical system with impulse. The main results are obtained by using the generalized fractional calculus and fixed point theory. Finally, a pair of examples are equipped to demonstrate the importance of the obtained theoretical result. The homotopy perturbation method (HPM) is successfully used in the numerical example.On a heavy-tailed distribution and the stability of an equilibrium in a distributed delay symmetric networkhttps://zbmath.org/1500.930432023-01-20T17:58:23.823708Z"Ncube, Israel"https://zbmath.org/authors/?q=ai:ncube.israelSummary: We consider a static artificial neural network model endowed with multiple unbounded S-type distributed time delays. The delay kernels are described by the Pareto distribution, which is a heavy-tailed power-law probability distribution frequently employed in the characterisation of many observable phenomena. We give a characterisation of the effects of the shape and the scale of the Pareto delay distribution on the stability of an equilibrium of the network.Chaos control of small-scale UAV helicopter based on high order differential feedback controllerhttps://zbmath.org/1500.930792023-01-20T17:58:23.823708Z"Guo, Xitong"https://zbmath.org/authors/?q=ai:guo.xitong"Qi, Guoyuan"https://zbmath.org/authors/?q=ai:qi.guoyuan"Li, Xia"https://zbmath.org/authors/?q=ai:li.xia.2"Ma, Shengli"https://zbmath.org/authors/?q=ai:ma.shengliSummary: The small-scale unmanned aerial vehicle (UAV) helicopter has a complex structure, strong nonlinearity, coupling and open-loop instability, making it shake violently and even produce chaotic oscillation under wind disturbances and improper configuration. The chaotic angular velocity dynamic model of the UAV helicopter is analysed via two cases. The sliding mode controller (SMC) relying on the linearised model, the PID controller, and the high order differential feedback controller (HODFC) not relying on the model are designed. The closed-loop system stability under both SMC and HODFC are analysed. The HODFC with a control filtering can actively reject the disturbance and uncertainty. The control performance of HODFC is superior to SMC and PID controllers. The SMC and HODFC can stabilise the chaotic oscillations of UAV helicopter's angular velocity, whereas the PID controller fails, and the HODFC control effect is superior to the SMC for disturbance rejection, uncertainty and linearisation bias in steady-state errors.Global quasi-synchronization of complex-valued recurrent neural networks with time-varying delay and interaction termshttps://zbmath.org/1500.931292023-01-20T17:58:23.823708Z"Kumar, Ankit"https://zbmath.org/authors/?q=ai:kumar.ankit"Das, Subir"https://zbmath.org/authors/?q=ai:das.subir-k"Yadav, Vijay K."https://zbmath.org/authors/?q=ai:yadav.vijay-kumar"Rajeev"https://zbmath.org/authors/?q=ai:rajeev.meenakshi|rajeev.v-r|rajeev.karthik|rajeev.varun|rajeev.bhaskaran|rajeev.tiwari|rajeev.sarada-gSummary: In this article, the global quasi-synchronization of complex-valued recurrent neural networks (CVRNNs) with time-varying delays and interaction terms has been investigated. It is based on the standard Lyapunov stability theory and matrix measure method employed with the nonlinear Lipschitz activation functions. A sufficient condition for global quasi-synchronization of the complex-valued recurrent neural network model is shown in an effective way through a proper description of Lyapunov-stability technique. This article provides quite a new result for the CVRNNs having time-varying delays and interaction terms. Finally, a numerical example is considered to show the viability and unwavering quality of our theoretical results under several conditions.