SIAM Journal on Applied Dynamical Systems Short Title: SIAM J. Appl. Dyn. Syst. Publisher: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA ISSN: 1536-0040/e Online: http://epubs.siam.org/loi/sjaday Comments: Indexed cover-to-cover; Published electronic only as of Vol. 1 (2002). Documents Indexed: 1,202 Publications (since 2002) References Indexed: 651 Publications with 27,639 References. all top 5 Latest Issues 21, No. 4 (2022) 21, No. 3 (2022) 21, No. 2 (2022) 21, No. 1 (2022) 20, No. 4 (2021) 20, No. 3 (2021) 20, No. 2 (2021) 20, No. 1 (2021) 19, No. 4 (2020) 19, No. 3 (2020) 19, No. 2 (2020) 19, No. 1 (2020) 18, No. 4 (2019) 18, No. 3 (2019) 18, No. 2 (2019) 18, No. 1 (2019) 17, No. 4 (2018) 17, No. 3 (2018) 17, No. 2 (2018) 17, No. 1 (2018) 16, No. 4 (2017) 16, No. 3 (2017) 16, No. 2 (2017) 16, No. 1 (2017) 15, No. 4 (2016) 15, No. 3 (2016) 15, No. 2 (2016) 15, No. 1 (2016) 14, No. 4 (2015) 14, No. 3 (2015) 14, No. 2 (2015) 14, No. 1 (2015) 13, No. 4 (2014) 13, No. 3 (2014) 13, No. 2 (2014) 13, No. 1 (2014) 12, No. 4 (2013) 12, No. 3 (2013) 12, No. 2 (2013) 12, No. 1 (2013) 11, No. 4 (2012) 11, No. 3 (2012) 11, No. 2 (2012) 11, No. 1 (2012) 10, No. 4 (2011) 10, No. 3 (2011) 10, No. 2 (2011) 10, No. 1 (2011) 9, No. 4 (2010) 9, No. 3 (2010) 9, No. 2 (2010) 9, No. 1 (2010) 8, No. 4 (2009) 8, No. 3 (2009) 8, No. 2 (2009) 8, No. 1 (2009) 7, No. 4 (2008) 7, No. 3 (2008) 7, No. 2 (2008) 7, No. 1 (2008) 6, No. 4 (2007) 6, No. 3 (2007) 6, No. 2 (2007) 6, No. 1 (2007) 5, No. 4 (2006) 5, No. 3 (2006) 5, No. 2 (2006) 5, No. 1 (2006) 4, No. 4 (2005) 4, No. 3 (2005) 4, No. 2 (2005) 4, No. 1 (2005) 3, No. 4 (2004) 3, No. 3 (2004) 3, No. 2 (2004) 3, No. 1 (2004) 2, No. 4 (2003) 2, No. 3 (2003) 2, No. 2 (2003) 2, No. 1 (2003) 1, No. 2 (2002) 1, No. 1 (2002) all top 5 Authors 24 Krauskopf, Bernd 18 Osinga, Hinke Maria 15 Rubin, Jonathan E. 14 Uldall Kristiansen, K. 14 Ward, Michael J. 13 Bressloff, Paul C. 13 Champneys, Alan R. 13 Guckenheimer, John M. 13 Kutz, J. Nathan 12 Golubitsky, Martin A. 12 Ha, Seung-Yeal 12 Meiss, James D. 11 Mischaikow, Konstantin 11 Wechselberger, Martin 10 Rademacher, Jens Diederich Michael 10 Sandstede, Björn 9 Bollt, Erik M. 9 de la Llave, Rafael 9 Doelman, Arjen 9 Hogan, S. John 9 Mireles-James, Jason D. 8 Brunton, Steven L. 8 Ermentrout, Bard G. 8 Ermentrout, George Bard 8 Kilpatrick, Zachary P. 8 Kirk, Vivien 8 Kolokolnikov, Theodore 8 Lessard, Jean-Philippe 8 Mezić, Igor 8 Moehlis, Jeff 8 Pelinovsky, Dmitry Efimovich 8 Porter, Mason Alexander 7 Clément, Frédérique 7 Desroches, Mathieu 7 Gedeon, Tomáš 7 Holmes, Philip J. 7 Kevrekidis, Ioannis George 7 Kevrekidis, Panayotis G. 7 Knobloch, Edgar 7 Postlethwaite, Claire M. 7 Scheel, Arnd 7 Wilson, Dan D. 7 Zgliczyński, Piotr 6 Ashwin, Peter 6 Coombes, Stephen 6 Dullin, Holger R. 6 Kopell, Nancy J. 6 Kühn, Christian 6 Palacián, Jesús F. 6 Rucklidge, Alastair M. 6 Stewart, Ian Nicholas 6 Terman, David Hillel 6 van den Berg, Jan Bouwe 6 Wilczak, Daniel 6 Yanchuk, Sergiĭ Volodymyrovych 6 Yanguas, Patricia 6 Yorke, James Alan 5 Avitabile, Daniele 5 Balasuriya, Sanjeeva 5 Colombo, Alessandro G. 5 Cummins, Bree 5 Fetecau, Razvan C. 5 Folias, Stefanos E. 5 Froyland, Gary 5 Giesl, Peter 5 Gottwald, Georg A. 5 Kuznetsov, Yuri Alexandrovich 5 Lee, Euiwoo 5 Lewis, Mark Alun 5 Lewis, Timothy J. 5 Lloyd, David J. B. 5 Mrozek, Marian 5 Rom-Kedar, Vered 5 Rotstein, Horacio G. 5 Rowley, Clarence W. 5 Sieber, Jan 5 Teixeira, Marco Antonio 5 Wanner, Thomas 5 Wayne, Clarence Eugene 5 Wulff, Claudia 4 Atay, Fatihcan M. 4 Beck, Margaret 4 Bertram, Richard 4 Booth, Victoria 4 Bose, Amitabha 4 Buono, Pietro-Luciano 4 Capinski, Maciej J. 4 Chow, Carson C. 4 Cors, Josep Maria 4 Dankowicz, Harry J. 4 Dawes, Jonathan H. P. 4 Day, Sarah L. 4 di Bernardo, Mario 4 Dias, Ana Paula S. 4 Diniz Behn, Cecilia G. 4 Faye, Grégory 4 Hafstein, Sigurður Freyr 4 Hüls, Thorsten 4 Hupkes, Hermen Jan 4 Jeffrey, Mike R. ...and 1,819 more Authors all top 5 Fields 686 Dynamical systems and ergodic theory (37-XX) 509 Ordinary differential equations (34-XX) 355 Biology and other natural sciences (92-XX) 286 Partial differential equations (35-XX) 177 Numerical analysis (65-XX) 157 Mechanics of particles and systems (70-XX) 73 Fluid mechanics (76-XX) 72 Systems theory; control (93-XX) 68 Probability theory and stochastic processes (60-XX) 42 Statistical mechanics, structure of matter (82-XX) 33 Optics, electromagnetic theory (78-XX) 32 Mechanics of deformable solids (74-XX) 30 Computer science (68-XX) 29 Combinatorics (05-XX) 27 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 26 Operations research, mathematical programming (90-XX) 24 Difference and functional equations (39-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 22 Integral equations (45-XX) 22 Statistics (62-XX) 19 Operator theory (47-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 18 Classical thermodynamics, heat transfer (80-XX) 13 Information and communication theory, circuits (94-XX) 12 Geophysics (86-XX) 9 Quantum theory (81-XX) 8 General topology (54-XX) 7 Convex and discrete geometry (52-XX) 7 Differential geometry (53-XX) 6 Group theory and generalizations (20-XX) 6 Approximations and expansions (41-XX) 6 Algebraic topology (55-XX) 6 Manifolds and cell complexes (57-XX) 6 Global analysis, analysis on manifolds (58-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Measure and integration (28-XX) 3 Algebraic geometry (14-XX) 3 Functional analysis (46-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Mathematical logic and foundations (03-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 1,004 Publications have been cited 10,981 times in 6,907 Documents Cited by ▼ Year ▼ Basic reproduction numbers for reaction-diffusion epidemic models. Zbl 1259.35120Wang, Wendi; Zhao, Xiao-Qiang 232 2012 Wave structure and nonlinear balances in a family of evolutionary PDEs. Zbl 1088.76531Holm, Darryl D.; Staley, Martin F. 134 2003 Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032Stewart, Ian; Golubitsky, Martin; Pivato, Marcus 120 2003 On the critical coupling for Kuramoto oscillators. Zbl 1242.34096Dörfler, Florian; Bullo, Francesco 115 2011 Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030Golubitsky, Martin; Stewart, Ian; Török, Andrei 115 2005 Canonical discontinuous planar piecewise linear systems. Zbl 1242.34020Freire, Emilio; Ponce, Enrique; Torres, Francisco 113 2012 Global synchronization of linearly hybrid coupled networks with time-varying delay. Zbl 1161.94011Yu, Wenwu; Cao, Jinde; Lü, Jinhu 105 2008 Existence and bifurcation of canards in \(\mathbb R^3\) in the case of a folded node. Zbl 1090.34047Wechselberger, Martin 97 2005 Sufficient conditions for fast switching synchronization in time-varying network topologies. Zbl 1145.37345Stilwell, Daniel J.; Bollt, Erik M.; Roberson, D. Gray 80 2006 Dynamic mode decomposition with control. Zbl 1334.65199Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 75 2016 Spatiotemporal dynamics of the diffusive mussel-algae model near Turing-Hopf bifurcation. Zbl 1382.35035Song, Yongli; Jiang, Heping; Liu, Quan-Xing; Yuan, Yuan 64 2017 Neuronal networks with gap junctions: a study of piecewise linear planar neuron models. Zbl 1159.92008Coombes, S. 62 2008 Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator. Zbl 1381.37096Arbabi, Hassan; Mezić, Igor 62 2017 PDE methods for nonlocal models. Zbl 1088.34011Laing, Carlo R.; Troy, William C. 61 2003 A primer of swarm equilibria. Zbl 1255.35012Bernoff, Andrew J.; Topaz, Chad M. 60 2011 A vaccination model for transmission dynamics of influenza. Zbl 1067.92051Alexander, M. E.; Bowman, C.; Moghadas, S. M.; Summers, R.; Gumel, A. B.; Sahai, B. M. 57 2004 Nonlinear patterns in urban crime: hotspots, bifurcations, and suppression. Zbl 1282.91273Short, M. B.; Bertozzi, A. L.; Brantingham, P. J. 56 2010 Mixed-mode oscillations in three time-scale systems: a prototypical example. Zbl 1167.34346Krupa, Martin; Popović, Nikola; Kopell, Nancy 55 2008 Evans functions for integral neural field equations with Heaviside firing rate function. Zbl 1067.92019Coombes, S.; Owen, M. R. 53 2004 Global phase-locking in finite populations of phase-coupled oscillators. Zbl 1167.34330Verwoerd, Mark; Mason, Oliver 52 2008 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025Guckenheimer, John 52 2008 A database schema for the analysis of global dynamics of multiparameter systems. Zbl 1186.37021Arai, Zin; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Pilarczyk, Paweł 51 2009 Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C. 51 2005 Localized hexagon patterns of the planar Swift-Hohenberg equation. Zbl 1168.35311Lloyd, David J. B.; Sandstede, Björn; Avitabile, Daniele; Champneys, Alan R. 50 2008 Classification of asymptotic behavior in a stochastic SIR model. Zbl 1343.34109Dieu, N. T.; Nguyen, D. H.; Du, N. H.; Yin, G. 50 2016 Projecting to a slow manifold: singularly perturbed systems and legacy codes. Zbl 1170.34343Gear, C. W.; Kaper, T. J.; Kevrekidis, I. G.; Zagaris, A. 50 2005 On the implementation of the 0-1 test for chaos. Zbl 1161.37054Gottwald, Georg A.; Melbourne, Ian 49 2009 A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity. Zbl 1210.37062Haro, A.; de la Llave, R. 48 2007 Defects in oscillatory media: toward a classification. Zbl 1059.37062Sandstede, Björn; Scheel, Arnd 48 2004 A computational and geometric approach to phase resetting curves and surfaces. Zbl 1216.34030Guillamon, Antoni; Huguet, Gemma 46 2009 Breathing pulses in an excitatory neural network. Zbl 1058.92010Folias, Stefanos E.; Bressloff, Paul C. 46 2004 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 44 2003 A geometric approach to the global attractor conjecture. Zbl 1301.34063Gopalkrishnan, Manoj; Miller, Ezra; Shiu, Anne 44 2014 \(R_0\) analysis of a spatiotemporal model for a stream population. Zbl 1252.35068Mckenzie, H. W.; Jin, Y.; Jacobsen, J.; Lewis, M. A. 43 2012 Random attractors for delay parabolic equations with additive noise and deterministic nonautonomous forcing. Zbl 1317.60081Wang, Xiaohu; Lu, Kening; Wang, Bixiang 42 2015 Multiresolution dynamic mode decomposition. Zbl 1338.37121Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. 42 2016 HJB-POD-based feedback design for the optimal control of evolution problems. Zbl 1058.35061Kunisch, K.; Volkwein, S.; Xie, L. 42 2004 Nondeterministic chaos, and the two-fold singularity in piecewise smooth flows. Zbl 1227.34044Colombo, Alessandro; Jeffrey, Mike R. 41 2011 A discrete data assimilation scheme for the solutions of the two-dimensional Navier-Stokes equations and their statistics. Zbl 1362.35208Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 41 2016 Freezing solutions of equivariant evolution equations. Zbl 1061.65078Beyn, W.-J.; Thümmler, V. 40 2004 The two-fold singularity of discontinuous vector fields. Zbl 1178.34042Jeffrey, M. R.; Colombo, A. 39 2009 Asymptotic dynamics of attractive-repulsive swarms. Zbl 1168.92045Leverentz, Andrew J.; Topaz, Chad M.; Bernoff, Andrew J. 39 2009 The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033Chen, W.; Ward, M. J. 39 2011 On computing the critical coupling coefficient for the Kuramoto model on a complete bipartite graph. Zbl 1167.34331Verwoerd, Mark; Mason, Oliver 38 2009 Nonsmooth Lagrangian mechanics and variational collision integrators. Zbl 1088.37045Fetecau, R. C.; Marsden, J. E.; Ortiz, M.; West, M. 38 2003 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005Guckenheimer, John; Oliva, Ricardo A. 38 2002 Power-law kinetics and determinant criteria for the preclusion of multistationarity in networks of interacting species. Zbl 1278.92012Wiuf, Carsten; Feliu, Elisenda 37 2013 Complete entrainment of Lohe oscillators under attractive and repulsive couplings. Zbl 1310.34060Choi, Sun-Ho; Ha, Seung-Yeal 37 2014 Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters \(H\in(1/3,1/2]\). Zbl 1336.60103Garrido-Atienza, María J.; Lu, Kening; Schmalfuss, Björn 36 2016 Higher order dynamic mode decomposition. Zbl 1373.37169Le Clainche, Soledad; Vega, José M. 36 2017 Study of singularities in nonsmooth dynamical systems via singular perturbation. Zbl 1167.34304Llibre, Jaume; Da Silva, Paulo R.; Teixeira, Marco A. 35 2009 Dynamics at a switching intersection: hierarchy, isonomy, and multiple sliding. Zbl 1310.34018Jeffrey, Mike R. 35 2014 Computation of mixed type functional differential boundary value problems. Zbl 1090.65093Abell, Kate A.; Elmer, Christopher E.; Humphries, A. R.; Van Vleck, Erik S. 35 2005 Noise-induced behaviors in neural mean field dynamics. Zbl 1235.92016Touboul, Jonathan; Hermann, Geoffroy; Faugeras, Olivier 35 2012 To snake or not to snake in the planar Swift-Hohenberg equation. Zbl 1200.37014Avitabile, Daniele; Lloyd, David J. B.; Burke, John; Knobloch, Edgar; Sandstede, Björn 34 2010 Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system. Zbl 1167.34361Abaid, Nicole; Eisenberg, Robert S.; Liu, Weishi 34 2008 Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. Zbl 1302.35386Burger, Martin; Fetecau, Razvan; Huang, Yanghong 34 2014 Stationary coexistence of hexagons and rolls via rigorous computations. Zbl 1371.37036van den Berg, Jan Bouwe; Deschênes, Andréa; Lessard, Jean-Philippe; Mireles James, Jason D. 33 2015 Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. Zbl 1058.35050Day, Sarah; Hiraoka, Yasuaki; Mischaikow, Konstantin; Ogawa, Toshiyuki 33 2005 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060Guckenheimer, John; Kuehn, Christian 32 2010 Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. Zbl 1330.37029Mireles James, J. D.; Mischaikow, Konstantin 32 2013 Bifurcations in delay differential equations and applications to tumor and immune system interaction models. Zbl 1284.34118Bi, Ping; Ruan, Shigui 32 2013 Parameterization of invariant manifolds for periodic orbits. I: Efficient numerics via the Floquet normal form. Zbl 1376.37057Castelli, Roberto; Lessard, Jean-Philippe; Mireles James, J. D. 32 2015 Uniform attractors for nonautonomous wave equations with nonlinear damping. Zbl 1210.35160Sun, Chunyou; Cao, Daomin; Duan, Jinqiao 32 2007 Front propagation in stochastic neural fields. Zbl 1246.92004Bressloff, Paul C.; Webber, Matthew A. 32 2012 Existence and stability of standing pulses in neural networks. I: Existence. Zbl 1109.34002Guo, Yixin; Chow, Carson C. 32 2005 Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. Zbl 1447.65119Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M. 32 2020 Integration of dissipative partial differential equations: a case study. Zbl 1298.37071Arioli, Gianni; Koch, Hans 31 2010 Wandering bumps in stochastic neural fields. Zbl 1278.92007Kilpatrick, Zachary P.; Ermentrout, Bard 31 2013 Speeds of spread and propagation for KPP models in time almost and space periodic media. Zbl 1172.35423Huang, Jianhua; Shen, Wenxian 31 2009 The slow dynamics of two-spike solutions for the Gray-Scott and Gierer-Meinhardt systems: competition and oscillatory instabilities. Zbl 1145.35404Sun, Wentao; Ward, Michael J.; Russell, Robert 31 2005 The Melnikov method and subharmonic orbits in a piecewise-smooth system. Zbl 1262.37028Granados, A.; Hogan, S. J.; Seara, T. M. 31 2012 Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse. Zbl 1059.37067England, J. P.; Krauskopf, B.; Osinga, H. M. 31 2004 Local/global analysis of the stationary solutions of some neural field equations. Zbl 1194.92015Veltz, Romain; Faugeras, Olivier 30 2010 An analytical approach to codimension-2 sliding bifurcations in the dry-friction oscillator. Zbl 1201.37086Guardia, Marcel; Hogan, S. John; Seara, Tere M. 30 2010 Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation. Zbl 1408.37062van den Berg, Jan Bouwe; Lessard, Jean-Philippe 30 2008 Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model. Zbl 1167.34353Rotstein, Horacio G.; Wechselberger, Martin; Kopell, Nancy 30 2008 Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108Huguet, Gemma; de la Llave, Rafael 30 2013 Computing slow manifolds of saddle type. Zbl 1176.37026Guckenheimer, John; Kuehn, Christian 30 2009 On the use of blowup to study regularizations of singularities of piecewise smooth dynamical systems in \(\mathbb{R}^3\). Zbl 1370.37100Kristiansen, K. Uldall; Hogan, S. J. 30 2015 Neural fields with distributed transmission speeds and long-range feedback delays. Zbl 1210.34118Atay, Fatihcan M.; Hutt, Axel 30 2006 An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedbacks. Zbl 1210.34086Xu, Jian; Chung, Kwok-Wai; Chan, Chuen-Lit 30 2007 Random attractor for damped nonlinear wave equations with white noise. Zbl 1094.35154Zhou, Shengfan; Yin, Fuqi; Ouyang, Zigen 30 2005 Kink-antikink collisions in the \(\phi^4\) equation: the \(n\)-bounce resonance and the separatrix map. Zbl 1145.74370Goodman, Roy H.; Haberman, Richard 30 2005 Continuation of quasi-periodic invariant tori. Zbl 1090.37057Schilder, Frank; Osinga, Hinke M.; Vogt, Werner 30 2005 Homoclinic stripe patterns. Zbl 1004.35063Doelman, Arjen; van der Ploeg, Harmen 30 2002 TC-HAT (\(\widehat{TC}\)): a novel toolbox for the continuation of periodic trajectories in hybrid dynamical systems. Zbl 1192.34004Thota, Phanikrishna; Dankowicz, Harry 29 2008 Data-driven identification of parametric partial differential equations. Zbl 1456.65096Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan 29 2019 Semistrong pulse interactions in a class of coupled reaction-diffusion equations. Zbl 1088.35517Doelman, Arjen; Kaper, Tasso J. 29 2003 Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart 28 2007 Some canonical bifurcations in the Swift-Hohenberg equation. Zbl 1210.34028Peletier, L. A.; Williams, J. F. 28 2007 Poisson-Nernst-Planck systems for ion flow with a local hard-sphere potential for ion size effects. Zbl 1284.34078Lin, Guojian; Liu, Weishi; Yi, Yingfei; Zhang, Mingji 27 2013 The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng 27 2006 Linearly recurrent autoencoder networks for learning dynamics. Zbl 1489.65164Otto, Samuel E.; Rowley, Clarence W. 27 2019 A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems. Zbl 1059.37068Day, S.; Junge, O.; Mischaikow, K. 27 2004 Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis. Zbl 1352.34101Breda, D.; Diekmann, O.; Gyllenberg, M.; Scarabel, F.; Vermiglio, R. 27 2016 The geometry of slow manifolds near a folded node. Zbl 1167.34365Desroches, M.; Krauskopf, B.; Osinga, H. M. 26 2008 On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain. Zbl 1267.35027Cvitanović, Predrag; Davidchack, Ruslan L.; Siminos, Evangelos 26 2010 Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems. Zbl 1354.37078Brunton, Steven L.; Tu, Jonathan H.; Bright, Ido; Kutz, J. Nathan 26 2014 The structure of MESSI biological systems. Zbl 1395.92071Pérez Millán, Mercedes; Dickenstein, Alicia 26 2018 Derivative-free Bayesian inversion using multiscale dynamics. Zbl 1493.62132Pavliotis, G. A.; Stuart, A. M.; Vaes, U. 4 2022 On a competition-diffusion-advection system from river ecology: mathematical analysis and numerical study. Zbl 1484.35034Yan, Xiao; Nie, Hua; Zhou, Peng 4 2022 Graphop mean-field limits for Kuramoto-type models. Zbl 1483.35270Gkogkas, Marios Antonios; Kuehn, Christian 2 2022 Dynamics of small particle inertial migration in curved square ducts. Zbl 1486.76098Ha, Kyung; Harding, Brendan; Bertozzi, Andrea L.; Stokes, Yvonne M. 2 2022 A dynamical theory for singular stochastic delay differential equations. I: Linear equations and a multiplicative ergodic theorem on fields of Banach spaces. Zbl 1490.34103Varzaneh, M. Ghani; Riedel, S.; Scheutzow, M. 2 2022 A bounded-confidence model of opinion dynamics on hypergraphs. Zbl 1482.91163Hickok, Abigail; Kureh, Yacoub; Brooks, Heather Z.; Feng, Michelle; Porter, Mason A. 1 2022 An adaptive phase-amplitude reduction framework without \(\mathcal{O}(\epsilon)\) constraints on inputs. Zbl 1490.34045Wilson, Dan 1 2022 Canards underlie both electrical and \(\mathrm{Ca}^{2+}\)-induced early afterdepolarizations in a model for cardiac myocytes. Zbl 1498.37129Kimrey, Joshua; Vo, Theodore; Bertram, Richard 1 2022 Emergent behaviors of rotation matrix flocks. Zbl 07537151Fetecau, Razvan C.; Ha, Seung-Yeal; Park, Hansol 1 2022 Ensemble inference methods for models with noisy and expensive likelihoods. Zbl 1493.62124Dunbar, Oliver R. A.; Duncan, Andrew B.; Stuart, Andrew M.; Wolfram, Marie-Therese 1 2022 Sequential attractors in combinatorial threshold-linear networks. Zbl 1491.92037Parmelee, Caitlyn; Alvarez, Juliana Londono; Curto, Carina; Morrison, Katherine 1 2022 Local and global existence for nonlocal multispecies advection-diffusion models. Zbl 1494.35002Giunta, Valeria; Hillen, Thomas; Lewis, Mark; Potts, Jonathan R. 1 2022 Modulation and amplitude equations on bounded domains for nonlinear SPDEs driven by cylindrical \(\alpha\)-stable Lévy processes. Zbl 1492.60197Yuan, Shenglan; Bloemker, Dirk 1 2022 Efficient computation of linear response of chaotic attractors with one-dimensional unstable manifolds. Zbl 1497.37103Chandramoorthy, Nisha; Wang, Qiqi 1 2022 Stochastically adaptive control and synchronization: from globally one-sided Lipschitzian to only locally Lipschitzian systems. Zbl 1492.60182Zhou, Shijie; Lai, Ying-Cheng; Lin, Wei 1 2022 Bifurcation sequences in a discontinuous piecewise-smooth map combining constant-catch and threshold-based harvesting strategies. Zbl 1484.92077Lois-Prados, Cristina; Hilker, Frank M. 1 2022 Dynamics of \(N\)-spot rings with oscillatory tails in a three-component reaction-diffusion system. Zbl 1497.35301Nishiura, Yasumasa; Xie, Shuangquan 1 2022 Bifurcations and dynamics in inertial focusing of particles in curved rectangular ducts. Zbl 07629774Valani, Rahil N.; Harding, Brendan; Stokes, Yvonne M. 1 2022 Periodic waves of the modified KdV equation as minimizers of a new variational problem. Zbl 07629779Le, Uyen; Pelinovsky, Dmitry E. 1 2022 A simple proof of asymptotic consensus in the Hegselmann-Krause and Cucker-Smale models with normalization and delay. Zbl 1466.34073Haskovec, Jan 7 2021 Symbolic proof of bistability in reaction networks. Zbl 1465.37105Torres, Angélica; Feliu, Elisenda 6 2021 Data assimilation for the Navier-Stokes equations using local observables. Zbl 1480.35309Biswas, Animikh; Bradshaw, Zachary; Jolly, Michael S. 5 2021 High-frequency instabilities of the Kawahara equation: a perturbative approach. Zbl 1478.35072Creedon, Ryan; Deconinck, Bernard; Trichtchenko, Olga 5 2021 Rigorous verification of Hopf bifurcations via desingularization and continuation. Zbl 1476.37094van den Berg, Jan Bouwe; Lessard, Jean-Philippe; Queirolo, Elena 4 2021 Nanoptera in weakly nonlinear woodpile chains and diatomic granular chains. 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Zbl 1443.34035Kim, Dohyun 2 2020 ...and 904 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 8,763 Authors 89 Ha, Seung-Yeal 50 Llibre, Jaume 45 Ward, Michael J. 43 Krauskopf, Bernd 42 Lessard, Jean-Philippe 37 Kühn, Christian 37 Mireles-James, Jason D. 37 Osinga, Hinke Maria 34 Kutz, J. Nathan 32 Bressloff, Paul C. 32 Wechselberger, Martin 31 Brunton, Steven L. 31 Kevrekidis, Ioannis George 31 Sandstede, Björn 30 Stewart, Ian Nicholas 29 Rubin, Jonathan E. 29 Scheel, Arnd 27 Carrillo de la Plata, José Antonio 27 Park, Hansol 26 de la Llave, Rafael 26 Zhao, Xiao-Qiang 25 Pelinovsky, Dmitry Efimovich 25 Teixeira, Marco Antonio 25 Wei, Juncheng 23 Coombes, Stephen 23 Desroches, Mathieu 23 Kevrekidis, Panayotis G. 23 Mezić, Igor 23 Mischaikow, Konstantin 23 Novaes, Douglas Duarte 23 Shen, Wenxian 22 Craciun, Gheorghe 22 Kolokolnikov, Theodore 22 Uldall Kristiansen, K. 21 Hupkes, Hermen Jan 21 Kim, Dohyun 21 Laing, Carlo R. 21 Ponce, Enrique 21 Wang, Bixiang 20 Adimy, Mostafa 20 Chen, Guanrong 20 van den Berg, Jan Bouwe 20 van Heijster, Peter 19 Ashwin, Peter 19 Balasuriya, Sanjeeva 19 Doelman, Arjen 19 Jeffrey, Mike R. 19 Knobloch, Edgar 19 Moehlis, Jeff 19 Porfiri, Maurizio 19 Zgliczyński, Piotr 18 Dias, Ana Paula S. 18 Fetecau, Razvan C. 18 Golubitsky, Martin A. 18 Kilpatrick, Zachary P. 18 Krupa, Martin 18 Wilson, Dan D. 17 Bollt, Erik M. 17 de Carvalho, Tiago 17 Faye, Grégory 17 Lawley, Sean D. 17 Sherratt, Jonathan A. 17 Simpson, David John Warwick 16 Aguiar, Manuela A. D. 16 Blömker, Dirk 16 Cai, Yongli 16 Duan, Jinqiao 16 Rademacher, Jens Diederich Michael 16 Wang, Weiming 16 Zhang, Mingji 15 Cao, Jinde 15 Gardini, Laura 15 Park, Jinyeong 15 Shi, Junping 15 Wang, Jinliang 15 Wanner, Thomas 15 Wyller, John A. 15 Xu, Jian 14 Belykh, Igor V. 14 Feliu, Elisenda 14 Froyland, Gary 14 Gedeon, Tomáš 14 Ghosh, Dibakar 14 Li, Zhuchun 14 Mrozek, Marian 14 M-Seara, Tere 14 Wu, Jianhong 13 Bi, Qinsheng 13 Crauste, Fabien 13 Huang, Lihong 13 Kaper, Tasso J. 13 Palacián, Jesús F. 13 Shiu, Anne 13 Sieber, Jan 13 Tonon, Durval José 13 Yang, Xiaosong 13 Yanguas, Patricia 12 Alla, Alessandro 12 Anderson, David Frederick 12 Bramburger, Jason J. ...and 8,663 more Authors all top 5 Cited in 493 Journals 423 SIAM Journal on Applied Dynamical Systems 361 Physica D 306 Chaos 289 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 271 Journal of Differential Equations 191 Discrete and Continuous Dynamical Systems. 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Mathematical, Physical and Engineering Sciences 16 International Journal of Biomathematics 15 Mathematical Methods in the Applied Sciences 15 Applied Numerical Mathematics 14 Japan Journal of Industrial and Applied Mathematics 14 Advances in Computational Mathematics 14 Journal of Mathematical Chemistry 14 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 14 Discrete Dynamics in Nature and Society 14 Kinetic and Related Models 13 Journal of Functional Analysis 13 Neural Networks 13 Journal of Mathematical Sciences (New York) 13 Foundations of Computational Mathematics 12 Ergodic Theory and Dynamical Systems 12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 11 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 11 Applied and Computational Harmonic Analysis 11 Journal of Physics A: Mathematical and Theoretical ...and 393 more Journals all top 5 Cited in 61 Fields 2,175 Biology and other natural sciences (92-XX) 2,153 Ordinary differential equations (34-XX) 2,106 Dynamical systems and ergodic theory (37-XX) 2,052 Partial differential equations (35-XX) 819 Numerical analysis (65-XX) 623 Systems theory; control (93-XX) 523 Mechanics of particles and systems (70-XX) 471 Fluid mechanics (76-XX) 431 Probability theory and stochastic processes (60-XX) 281 Statistical mechanics, structure of matter (82-XX) 194 Computer science (68-XX) 186 Calculus of variations and optimal control; optimization (49-XX) 183 Mechanics of deformable solids (74-XX) 164 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 139 Operations research, mathematical programming (90-XX) 130 Operator theory (47-XX) 122 Statistics (62-XX) 116 Integral equations (45-XX) 112 Combinatorics (05-XX) 101 Difference and functional equations (39-XX) 101 Information and communication theory, circuits (94-XX) 88 Optics, electromagnetic theory (78-XX) 82 Quantum theory (81-XX) 78 Classical thermodynamics, heat transfer (80-XX) 60 Global analysis, analysis on manifolds (58-XX) 59 Differential geometry (53-XX) 53 Geophysics (86-XX) 47 Linear and multilinear algebra; matrix theory (15-XX) 47 Real functions (26-XX) 23 Approximations and expansions (41-XX) 22 Algebraic topology (55-XX) 18 Commutative algebra (13-XX) 17 General and overarching topics; collections (00-XX) 17 Special functions (33-XX) 17 Functional analysis (46-XX) 17 Convex and discrete geometry (52-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 16 Relativity and gravitational theory (83-XX) 15 Algebraic geometry (14-XX) 15 General topology (54-XX) 15 Astronomy and astrophysics (85-XX) 12 Measure and integration (28-XX) 12 Manifolds and cell complexes (57-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 Group theory and generalizations (20-XX) 10 Field theory and polynomials (12-XX) 7 Topological groups, Lie groups (22-XX) 6 Number theory (11-XX) 5 History and biography (01-XX) 5 Potential theory (31-XX) 4 Mathematical logic and foundations (03-XX) 4 Functions of a complex variable (30-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Geometry (51-XX) 2 Category theory; homological algebra (18-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mathematics education (97-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) Citations by Year