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: 1,064 Publications (since 2002) References Indexed: 513 Publications with 21,427 References. all top 5 Latest Issues 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 14 Ward, Michael J. 13 Bressloff, Paul C. 13 Champneys, Alan R. 13 Guckenheimer, John M. 12 Golubitsky, Martin A. 12 Kutz, J. Nathan 11 Meiss, James D. 10 Rubin, Jonathan E. 10 Sandstede, Björn 10 Wechselberger, Martin 9 Doelman, Arjen 9 Ha, Seung-Yeal 9 Mireles-James, Jason D. 9 Mischaikow, Konstantin 9 Rademacher, Jens Diederich Michael 8 Bollt, Erik M. 8 Brunton, Steven L. 8 de la Llave, Rafael 8 Kolokolnikov, Theodore 8 Lessard, Jean-Philippe 8 Moehlis, Jeff 7 Desroches, Mathieu 7 Ermentrout, Bard G. 7 Holmes, Philip J. 7 Kevrekidis, Ioannis George 7 Kevrekidis, Panayotis G. 7 Kilpatrick, Zachary P. 7 Kirk, Vivien 7 Knobloch, Edgar 7 Pelinovsky, Dmitry Efimovich 7 Postlethwaite, Claire M. 7 Zgliczyński, Piotr 6 Ashwin, Peter 6 Clément, Frédérique 6 Dullin, Holger R. 6 Hogan, S. John 6 Kopell, Nancy J. 6 Mezić, Igor 6 Scheel, Arnd 6 Stewart, Ian Nicholas 6 van den Berg, Jan Bouwe 6 Wilczak, Daniel 6 Yorke, James Alan 5 Colombo, Alessandro G. 5 Folias, Stefanos E. 5 Gedeon, Tomáš 5 Gottwald, Georg A. 5 Kuznetsov, Yuri Alexandrovich 5 Lloyd, David J. B. 5 Palacián, Jesús F. 5 Rowley, Clarence W. 5 Rucklidge, Alastair M. 5 Sieber, Jan 5 Uldall Kristiansen, K. 5 Wanner, Thomas 5 Wayne, Clarence Eugene 5 Wulff, Claudia 5 Yanguas, Patricia 4 Atay, Fatihcan M. 4 Avitabile, Daniele 4 Balasuriya, Sanjeeva 4 Bose, Amitabha 4 Buono, Pietro-Luciano 4 Capinski, Maciej J. 4 Chow, Carson C. 4 Coombes, Stephen 4 Cors, Josep Maria 4 Cummins, Bree 4 Dankowicz, Harry J. 4 Dawes, Jonathan H. P. 4 Day, Sarah L. 4 di Bernardo, Mario 4 Faye, Grégory 4 Fetecau, Razvan C. 4 Froyland, Gary 4 Hupkes, Hermen Jan 4 Jeffrey, Mike R. 4 Keener, James P. 4 Kristiansen, Kristian Uldall 4 Kühn, Christian 4 Laing, Carlo R. 4 Lewis, Timothy J. 4 Mrozek, Marian 4 Neuberger, John M. 4 Oldeman, Bart E. 4 Porfiri, Maurizio 4 Porter, Mason Alexander 4 Rom-Kedar, Vered 4 Sepulchre, Rodolphe J. 4 Sieben, Nándor 4 Starke, Jens 4 Swift, James W. 4 Swigon, David 4 Szmolyan, Peter 4 Teixeira, Marco Antonio 4 Terman, David H. 4 Troy, William C. 4 Tzou, Justin C. ...and 1,554 more Authors all top 5 Fields 626 Dynamical systems and ergodic theory (37-XX) 466 Ordinary differential equations (34-XX) 309 Biology and other natural sciences (92-XX) 252 Partial differential equations (35-XX) 159 Numerical analysis (65-XX) 143 Mechanics of particles and systems (70-XX) 67 Fluid mechanics (76-XX) 59 Systems theory; control (93-XX) 55 Probability theory and stochastic processes (60-XX) 35 Statistical mechanics, structure of matter (82-XX) 29 Mechanics of deformable solids (74-XX) 29 Optics, electromagnetic theory (78-XX) 24 Operations research, mathematical programming (90-XX) 22 Integral equations (45-XX) 20 Difference and functional equations (39-XX) 19 Combinatorics (05-XX) 18 Operator theory (47-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 18 Computer science (68-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Statistics (62-XX) 16 Classical thermodynamics, heat transfer (80-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 11 Geophysics (86-XX) 10 Information and communication theory, circuits (94-XX) 8 General topology (54-XX) 8 Quantum theory (81-XX) 7 Differential geometry (53-XX) 6 Convex and discrete geometry (52-XX) 6 Manifolds and cell complexes (57-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Group theory and generalizations (20-XX) 5 Algebraic topology (55-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 3 Measure and integration (28-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Mathematical logic and foundations (03-XX) 1 Real functions (26-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 889 Publications have been cited 8,654 times in 5,495 Documents Cited by ▼ Year ▼ Basic reproduction numbers for reaction-diffusion epidemic models. Zbl 1259.35120Wang, Wendi; Zhao, Xiao-Qiang 154 2012 Wave structure and nonlinear balances in a family of evolutionary PDEs. Zbl 1088.76531Holm, Darryl D.; Staley, Martin F. 119 2003 Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032Stewart, Ian; Golubitsky, Martin; Pivato, Marcus 109 2003 Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030Golubitsky, Martin; Stewart, Ian; Török, Andrei 107 2005 On the critical coupling for Kuramoto oscillators. Zbl 1242.34096Dörfler, Florian; Bullo, Francesco 97 2011 Global synchronization of linearly hybrid coupled networks with time-varying delay. Zbl 1161.94011Yu, Wenwu; Cao, Jinde; Lü, Jinhu 97 2008 Existence and bifurcation of canards in \(\mathbb R^3\) in the case of a folded node. Zbl 1090.34047Wechselberger, Martin 87 2005 Canonical discontinuous planar piecewise linear systems. Zbl 1242.34020Freire, Emilio; Ponce, Enrique; Torres, Francisco 82 2012 Sufficient conditions for fast switching synchronization in time-varying network topologies. Zbl 1145.37345Stilwell, Daniel J.; Bollt, Erik M.; Roberson, D. Gray 74 2006 PDE methods for nonlocal models. Zbl 1088.34011Laing, Carlo R.; Troy, William C. 56 2003 Neuronal networks with gap junctions: a study of piecewise linear planar neuron models. Zbl 1159.92008Coombes, S. 54 2008 A primer of swarm equilibria. Zbl 1255.35012Bernoff, Andrew J.; Topaz, Chad M. 53 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. 49 2004 Projecting to a slow manifold: singularly perturbed systems and legacy codes. Zbl 1170.34343Gear, C. W.; Kaper, T. J.; Kevrekidis, I. G.; Zagaris, A. 49 2005 Global phase-locking in finite populations of phase-coupled oscillators. Zbl 1167.34330Verwoerd, Mark; Mason, Oliver 49 2008 Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C. 48 2005 Dynamic mode decomposition with control. Zbl 1334.65199Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 48 2016 Evans functions for integral neural field equations with Heaviside firing rate function. Zbl 1067.92019Coombes, S.; Owen, M. R. 47 2004 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025Guckenheimer, John 45 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 44 2009 Defects in oscillatory media: toward a classification. Zbl 1059.37062Sandstede, Björn; Scheel, Arnd 43 2004 Breathing pulses in an excitatory neural network. Zbl 1058.92010Folias, Stefanos E.; Bressloff, Paul C. 43 2004 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. 43 2007 A computational and geometric approach to phase resetting curves and surfaces. Zbl 1216.34030Guillamon, Antoni; Huguet, Gemma 41 2009 Localized hexagon patterns of the planar Swift-Hohenberg equation. Zbl 1168.35311Lloyd, David J. B.; Sandstede, Björn; Avitabile, Daniele; Champneys, Alan R. 41 2008 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 40 2003 Mixed-mode oscillations in three time-scale systems: a prototypical example. Zbl 1167.34346Krupa, Martin; Popović, Nikola; Kopell, Nancy 40 2008 On the implementation of the 0-1 test for chaos. Zbl 1161.37054Gottwald, Georg A.; Melbourne, Ian 40 2009 Nonlinear patterns in urban crime: hotspots, bifurcations, and suppression. Zbl 1282.91273Short, M. B.; Bertozzi, A. L.; Brantingham, P. J. 40 2010 Spatiotemporal dynamics of the diffusive mussel-algae model near Turing-Hopf bifurcation. Zbl 1382.35035Song, Yongli; Jiang, Heping; Liu, Quan-Xing; Yuan, Yuan 38 2017 HJB-POD-based feedback design for the optimal control of evolution problems. Zbl 1058.35061Kunisch, K.; Volkwein, S.; Xie, L. 36 2004 A geometric approach to the global attractor conjecture. Zbl 1301.34063Gopalkrishnan, Manoj; Miller, Ezra; Shiu, Anne 36 2014 Asymptotic dynamics of attractive-repulsive swarms. Zbl 1168.92045Leverentz, Andrew J.; Topaz, Chad M.; Bernoff, Andrew J. 35 2009 On computing the critical coupling coefficient for the Kuramoto model on a complete bipartite graph. Zbl 1167.34331Verwoerd, Mark; Mason, Oliver 35 2009 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005Guckenheimer, John; Oliva, Ricardo A. 34 2002 Freezing solutions of equivariant evolution equations. Zbl 1061.65078Beyn, W.-J.; Thümmler, V. 34 2004 The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033Chen, W.; Ward, M. J. 34 2011 Nonsmooth Lagrangian mechanics and variational collision integrators. Zbl 1088.37045Fetecau, R. C.; Marsden, J. E.; Ortiz, M.; West, M. 33 2003 \(R_0\) analysis of a spatiotemporal model for a stream population. Zbl 1252.35068Mckenzie, H. W.; Jin, Y.; Jacobsen, J.; Lewis, M. A. 33 2012 Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator. Zbl 1381.37096Arbabi, Hassan; Mezić, Igor 32 2017 Noise-induced behaviors in neural mean field dynamics. Zbl 1235.92016Touboul, Jonathan; Hermann, Geoffroy; Faugeras, Olivier 31 2012 Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. Zbl 1058.35050Day, Sarah; Hiraoka, Yasuaki; Mischaikow, Konstantin; Ogawa, Toshiyuki 31 2005 Existence and stability of standing pulses in neural networks. I: Existence. Zbl 1109.34002Guo, Yixin; Chow, Carson C. 31 2005 Computation of mixed type functional differential boundary value problems. Zbl 1090.65093Abell, Kate A.; Elmer, Christopher E.; Humphries, A. R.; Van Vleck, Erik S. 31 2005 Front propagation in stochastic neural fields. Zbl 1246.92004Bressloff, Paul C.; Webber, Matthew A. 30 2012 The two-fold singularity of discontinuous vector fields. Zbl 1178.34042Jeffrey, M. R.; Colombo, A. 30 2009 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. 30 2015 Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. Zbl 1330.37029Mireles James, J. D.; Mischaikow, Konstantin 30 2013 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 29 2005 Nondeterministic chaos, and the two-fold singularity in piecewise smooth flows. Zbl 1227.34044Colombo, Alessandro; Jeffrey, Mike R. 29 2011 Classification of asymptotic behavior in a stochastic SIR model. Zbl 1343.34109Dieu, N. T.; Nguyen, D. H.; Du, N. H.; Yin, G. 29 2016 Homoclinic stripe patterns. Zbl 1004.35063Doelman, Arjen; van der Ploeg, Harmen 28 2002 Semistrong pulse interactions in a class of coupled reaction-diffusion equations. Zbl 1088.35517Doelman, Arjen; Kaper, Tasso J. 28 2003 Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system. Zbl 1167.34361Abaid, Nicole; Eisenberg, Robert S.; Liu, Weishi 28 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 28 2008 Study of singularities in nonsmooth dynamical systems via singular perturbation. Zbl 1167.34304Llibre, Jaume; Da Silva, Paulo R.; Teixeira, Marco A. 28 2009 Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. Zbl 1302.35386Burger, Martin; Fetecau, Razvan; Huang, Yanghong 28 2014 Power-law kinetics and determinant criteria for the preclusion of multistationarity in networks of interacting species. Zbl 1278.92012Wiuf, Carsten; Feliu, Elisenda 28 2013 Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108Huguet, Gemma; de la Llave, Rafael 28 2013 Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse. Zbl 1059.37067England, J. P.; Krauskopf, B.; Osinga, H. M. 27 2004 Computing slow manifolds of saddle type. Zbl 1176.37026Guckenheimer, John; Kuehn, Christian 27 2009 Complete entrainment of Lohe oscillators under attractive and repulsive couplings. Zbl 1310.34060Choi, Sun-Ho; Ha, Seung-Yeal 27 2014 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 27 2010 Some canonical bifurcations in the Swift-Hohenberg equation. Zbl 1210.34028Peletier, L. A.; Williams, J. F. 27 2007 Multiresolution dynamic mode decomposition. Zbl 1338.37121Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. 27 2016 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. 27 2016 Local/global analysis of the stationary solutions of some neural field equations. Zbl 1194.92015Veltz, Romain; Faugeras, Olivier 26 2010 Dynamics at a switching intersection: hierarchy, isonomy, and multiple sliding. Zbl 1310.34018Jeffrey, Mike R. 26 2014 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. 26 2015 Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation. Zbl 1408.37062van den Berg, Jan Bouwe; Lessard, Jean-Philippe 26 2008 Neural fields with distributed transmission speeds and long-range feedback delays. Zbl 1210.34118Atay, Fatihcan M.; Hutt, Axel 26 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 26 2007 Random attractors for delay parabolic equations with additive noise and deterministic nonautonomous forcing. Zbl 1317.60081Wang, Xiaohu; Lu, Kening; Wang, Bixiang 26 2015 A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems. Zbl 1059.37068Day, S.; Junge, O.; Mischaikow, K. 25 2004 Continuation of quasi-periodic invariant tori. Zbl 1090.37057Schilder, Frank; Osinga, Hinke M.; Vogt, Werner 25 2005 Speeds of spread and propagation for KPP models in time almost and space periodic media. Zbl 1172.35423Huang, Jianhua; Shen, Wenxian 25 2009 Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart 25 2007 TC-HAT (\(\widehat{TC}\)): a novel toolbox for the continuation of periodic trajectories in hybrid dynamical systems. Zbl 1192.34004Thota, Phanikrishna; Dankowicz, Harry 25 2008 Integration of dissipative partial differential equations: a case study. Zbl 1298.37071Arioli, Gianni; Koch, Hans 25 2010 Continuation-based computation of global isochrons. Zbl 1232.37014Osinga, Hinke M.; Moehlis, Jeff 25 2010 An analytical approach to codimension-2 sliding bifurcations in the dry-friction oscillator. Zbl 1201.37086Guardia, Marcel; Hogan, S. John; Seara, Tere M. 25 2010 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 25 2006 Reliable computation of robust response tori on the verge of breakdown. Zbl 1253.37077Figueras, Jordi-Lluís; Haro, Àlex 24 2012 Bifurcations in delay differential equations and applications to tumor and immune system interaction models. Zbl 1284.34118Bi, Ping; Ruan, Shigui 24 2013 Kink-antikink collisions in the \(\phi^4\) equation: the \(n\)-bounce resonance and the separatrix map. Zbl 1145.74370Goodman, Roy H.; Haberman, Richard 23 2005 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 23 2014 Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster. Zbl 1263.37036Linaro, Daniele; Champneys, Alan; Desroches, Mathieu; Storace, Marco 23 2012 Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system. Zbl 1213.37046Wilczak, Daniel 23 2010 Front interactions in a three-component system. Zbl 1197.35047van Heijster, P.; Doelman, A.; Kaper, T. J.; Promislow, K. 23 2010 Uniform attractors for nonautonomous wave equations with nonlinear damping. Zbl 1210.35160Sun, Chunyou; Cao, Daomin; Duan, Jinqiao 23 2007 Computing geodesic level sets on global (un)stable manifolds of vector fields. Zbl 1089.37014Krauskopf, Bernd; Osinga, Hinke M. 22 2003 The forced van der Pol equation. II: Canards in the reduced system. Zbl 1089.37013Bold, Katherine; Edwards, Chantal; Guckenheimer, John; Guharay, Sabyasachi; Hoffman, Kathleen; Hubbard, Judith; Oliva, Ricardo; Weckesser, Warren 22 2003 Spiral waves in nonlocal equations. Zbl 1090.37056Laing, Carlo R. 22 2005 Random attractor for damped nonlinear wave equations with white noise. Zbl 1094.35154Zhou, Shengfan; Yin, Fuqi; Ouyang, Zigen 22 2005 Differential geometry perspective of shape coherence and curvature evolution by finite-time nonhyperbolic splitting. Zbl 1329.37031Ma, Tian; Bollt, Erik M. 22 2014 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. 22 2015 Periodic solutions in Hamiltonian systems, averaging, and the lunar problem. Zbl 1159.37424Yanguas, Patricia; Palacián, Jesús F.; Meyer, Kenneth R.; Dumas, H. Scott 22 2008 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060Guckenheimer, John; Kuehn, Christian 22 2010 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 22 2013 Scaling in singular perturbation problems: blowing up a relaxation oscillator. Zbl 1243.34066Kosiuk, Ilona; Szmolyan, Peter 21 2011 Symbolic proof of bistability in reaction networks. Zbl 1465.37105Torres, Angélica; Feliu, Elisenda 2 2021 Dynamic transitions and bifurcations for a class of axisymmetric geophysical fluid flow. Zbl 1461.76172Han, Daozhi; Hernandez, Marco; Wang, Quan 1 2021 Pseudospectral approximation of Hopf bifurcation for delay differential equations. Zbl 07335803de Wolff, B. A. J.; Scarabel, F.; Verduyn Lunel, S. M.; Diekmann, O. 1 2021 Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics. Zbl 07335807Longo, Iacopo P.; Núñez, Carmen; Obaya, Rafael; Rasmussen, Martin 1 2021 Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. Zbl 1447.65119Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M. 8 2020 Physics-informed probabilistic learning of linear embeddings of nonlinear dynamics with guaranteed stability. Zbl 1442.37090Pan, Shaowu; Duraisamy, Karthik 5 2020 From the Lohe tensor model to the Lohe Hermitian sphere model and emergent dynamics. Zbl 1441.82011Ha, Seung-Yeal; Park, Hansol 4 2020 Mathematical modeling for schistosomiasis with seasonal influence: a case study in Hubei, China. Zbl 1445.37074Zhang, Tailei; Zhao, Xiao-Qiang 4 2020 Robust feedback control of nonlinear PDEs by numerical approximation of high-dimensional Hamilton-Jacobi-Isaacs equations. Zbl 1443.49041Kalise, Dante; Kundu, Sudeep; Kunisch, Karl 4 2020 Barriers to the transport of diffusive scalars in compressible flows. Zbl 1448.76146Haller, George; Karrasch, Daniel; Kogelbauer, Florian 3 2020 Permanence of weakly reversible mass-action systems with a single linkage class. Zbl 1443.92110Boros, Balázs; Hofbauer, Josef 3 2020 Data assimilation in large Prandtl Rayleigh-Bénard convection from thermal measurements. Zbl 1434.76041Farhat, A.; Glatt-Holtz, N. E.; Martinez, V. R.; McQuarrie, S. A.; Whitehead, J. P. 3 2020 Time-delay observables for Koopman: theory and applications. Zbl 1441.37090Kamb, Mason; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan 3 2020 Computational singular perturbation method for nonstandard slow-fast systems. Zbl 1457.37102Lizarraga, Ian; Wechselberger, Martin 3 2020 Pulse solutions for an extended Klausmeier model with spatially varying coefficients. Zbl 1431.35071Bastiaansen, Robbin; Chirilus-Bruckner, Martina; Doelman, Arjen 2 2020 Data based reconstruction of duplex networks. Zbl 1437.37123Ma, Chuang; Chen, Han-Shuang; Li, Xiang; Lai, Ying-Cheng; Zhang, Hai-Feng 2 2020 Neurologically motivated coupling functions in models of motor coordination. Zbl 1446.34092Słowiński, Piotr; Al-Ramadhani, Sohaib; Tsaneva-Atanasova, Krasimira 2 2020 Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations. Zbl 07175469Bosschaert, Maikel M.; Janssens, Sebastiaan G.; Kuznetsov, Yu. A. 2 2020 Clamping and synchronization in the strongly coupled FitzHugh-Nagumo model. Zbl 1447.35335Quininao, Cristobal; Touboul, Jonathan D. 2 2020 Bifurcations on fully inhomogeneous networks. Zbl 1443.34039Gandhi, Punit; Golubitsky, Martin; Postlethwaite, Claire; Stewart, Ian; Wang, Yangyang 2 2020 On the Koopman operator of algorithms. Zbl 1437.47048Dietrich, Felix; Thiem, Thomas N.; Kevrekidis, Ioannis G. 2 2020 Intralayer synchronization in evolving multiplex hypernetworks: analytical approach. Zbl 1441.37093Rakshit, Sarbendu; Bera, Bidesh K.; Bollt, Erik M.; Ghosh, Dibakar 2 2020 Tipping phenomena and points of no return in ecosystems: beyond classical bifurcations. Zbl 1467.37091O’Keeffe, Paul E.; Wieczorek, Sebastian 2 2020 LOR for analysis of periodic dynamics: a one-stop shop approach. Zbl 1461.34065Letson, Benjamin; Rubin, Jonathan E. 1 2020 Synchronization in discrete-time, discrete-state random dynamical systems. Zbl 1433.37055Huang, Wen; Qian, Hong; Wang, Shirou; Ye, Felix X.-F.; Yi, Yingfei 1 2020 Conley index approach to sampled dynamics. Zbl 1442.37088Batko, Bogdan; Mischaikow, Konstantin; Mrozek, Marian; Przybylski, Mateusz 1 2020 Lotka-Volterra competition model on graphs. Zbl 1437.92103Slavík, Antonín 1 2020 Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear flow. 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Zbl 1396.34042Wang, Cheng; Zhang, Xiang 9 2018 ...and 789 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,007 Authors 69 Ha, Seung-Yeal 42 Llibre, Jaume 40 Ward, Michael J. 38 Krauskopf, Bernd 36 Osinga, Hinke Maria 35 Lessard, Jean-Philippe 32 Mireles-James, Jason D. 31 Bressloff, Paul C. 29 Kevrekidis, Ioannis George 29 Sandstede, Björn 29 Stewart, Ian Nicholas 28 Wechselberger, Martin 27 Kühn, Christian 27 Kutz, J. Nathan 26 Rubin, Jonathan E. 26 Scheel, Arnd 24 Carrillo de la Plata, José Antonio 23 Desroches, Mathieu 23 Zhao, Xiao-Qiang 22 Brunton, Steven L. 22 Pelinovsky, Dmitry Efimovich 21 de la Llave, Rafael 21 Laing, Carlo R. 21 Mezić, Igor 21 Shen, Wenxian 21 Wei, Juncheng 20 Coombes, Stephen 19 Hupkes, Hermen Jan 19 Kevrekidis, Panayotis G. 19 Knobloch, Edgar 19 Kolokolnikov, Theodore 19 Mischaikow, Konstantin 19 Moehlis, Jeff 19 Ponce, Enrique 18 Balasuriya, Sanjeeva 18 Doelman, Arjen 18 Krupa, Martin 18 Novaes, Douglas Duarte 18 van Heijster, Peter 18 Zgliczyński, Piotr 17 Adimy, Mostafa 17 Chen, Guanrong 17 Golubitsky, Martin A. 17 Jeffrey, Mike R. 17 Kilpatrick, Zachary P. 17 Porfiri, Maurizio 17 Wang, Bixiang 16 Ashwin, Peter 16 Bollt, Erik M. 16 Faye, Grégory 16 Kim, Dohyun 16 Sherratt, Jonathan A. 16 Teixeira, Marco Antonio 16 van den Berg, Jan Bouwe 15 Blömker, Dirk 15 Cao, Jinde 15 de Carvalho, Tiago 15 Dias, Ana Paula S. 15 Fetecau, Razvan C. 14 Belykh, Igor V. 14 Craciun, Gheorghe 14 Lawley, Sean D. 14 Park, Hansol 14 Park, Jinyeong 14 Rademacher, Jens Diederich Michael 14 Simpson, David John Warwick 14 Wyller, John A. 13 Aguiar, Manuela A. D. 13 Crauste, Fabien 13 Kaper, Tasso J. 13 Li, Zhuchun 13 Palacián, Jesús F. 13 Shi, Junping 13 Wilson, Dan D. 13 Yanguas, Patricia 13 Zhang, Mingji 12 Cai, Yongli 12 Duan, Jinqiao 12 Froyland, Gary 12 Lăzureanu, Cristian 12 Páez Chávez, Joseph Nikolai 12 M-Seara, Tere 12 Wang, Weiming 12 Wanner, Thomas 12 Xu, Jian 12 Yu, Wenwu 11 Alla, Alessandro 11 Barrio, Roberto 11 Feliu, Elisenda 11 Gardini, Laura 11 Giannakis, Dimitrios 11 Jiang, Jifa 11 Lee, Jaeseung 11 Liu, Weishi 11 Mrozek, Marian 11 Pilarczyk, Paweł 11 Ruan, Shigui 11 Shiu, Anne 11 Tonon, Durval José 11 Tzou, Justin C. ...and 6,907 more Authors all top 5 Cited in 424 Journals 334 SIAM Journal on Applied Dynamical Systems 306 Chaos 264 Physica D 259 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 229 Journal of Differential Equations 144 Journal of Nonlinear Science 135 Discrete and Continuous Dynamical Systems. 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Mathematical, Physical and Engineering Sciences 14 Advances in Computational Mathematics 14 Discrete Dynamics in Nature and Society 14 Networks and Heterogeneous Media 13 Physics Letters. A 13 SIAM Journal on Numerical Analysis 13 Neural Networks 13 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 12 Ergodic Theory and Dynamical Systems 12 Applied Numerical Mathematics 12 Japan Journal of Industrial and Applied Mathematics 12 Foundations of Computational Mathematics 12 Nonlinear Analysis. Hybrid Systems 12 SIAM/ASA Journal on Uncertainty Quantification 11 Mathematics and Computers in Simulation 11 Journal of Mathematical Chemistry 11 International Journal of Biomathematics 11 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Indagationes Mathematicae. New Series 10 Applied and Computational Harmonic Analysis 10 Journal of Mathematical Sciences (New York) 10 Journal of Applied Mathematics 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Journal of Physics A: Mathematical and Theoretical 9 Journal of Functional Analysis 9 Physics of Fluids ...and 324 more Journals all top 5 Cited in 59 Fields 1,757 Dynamical systems and ergodic theory (37-XX) 1,741 Ordinary differential equations (34-XX) 1,705 Biology and other natural sciences (92-XX) 1,584 Partial differential equations (35-XX) 638 Numerical analysis (65-XX) 494 Systems theory; control (93-XX) 431 Mechanics of particles and systems (70-XX) 360 Fluid mechanics (76-XX) 305 Probability theory and stochastic processes (60-XX) 193 Statistical mechanics, structure of matter (82-XX) 152 Mechanics of deformable solids (74-XX) 140 Calculus of variations and optimal control; optimization (49-XX) 120 Computer science (68-XX) 119 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 112 Operator theory (47-XX) 111 Operations research, mathematical programming (90-XX) 101 Integral equations (45-XX) 84 Statistics (62-XX) 83 Combinatorics (05-XX) 83 Difference and functional equations (39-XX) 81 Information and communication theory, circuits (94-XX) 69 Optics, electromagnetic theory (78-XX) 57 Classical thermodynamics, heat transfer (80-XX) 57 Quantum theory (81-XX) 53 Differential geometry (53-XX) 52 Global analysis, analysis on manifolds (58-XX) 41 Linear and multilinear algebra; matrix theory (15-XX) 41 Geophysics (86-XX) 30 Real functions (26-XX) 16 Algebraic topology (55-XX) 15 Approximations and expansions (41-XX) 14 Special functions (33-XX) 14 Harmonic analysis on Euclidean spaces (42-XX) 14 Convex and discrete geometry (52-XX) 14 Astronomy and astrophysics (85-XX) 13 Functional analysis (46-XX) 13 Relativity and gravitational theory (83-XX) 11 General and overarching topics; collections (00-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 Commutative algebra (13-XX) 10 Measure and integration (28-XX) 10 General topology (54-XX) 9 Group theory and generalizations (20-XX) 9 Manifolds and cell complexes (57-XX) 8 Algebraic geometry (14-XX) 6 Field theory and polynomials (12-XX) 6 Topological groups, Lie groups (22-XX) 5 History and biography (01-XX) 5 Number theory (11-XX) 3 Mathematical logic and foundations (03-XX) 3 Potential theory (31-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Category theory; homological algebra (18-XX) 2 Functions of a complex variable (30-XX) 2 Geometry (51-XX) 2 Mathematics education (97-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) Citations by Year