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: Journal; Indexed cover-to-cover; Published electronic only as of Vol. 1 (2002). Documents Indexed: 1,333 Publications (since 2002) References Indexed: 782 Publications with 33,571 References. all top 5 Latest Issues 23, No. 1 (2024) 22, No. 4 (2023) 22, No. 3 (2023) 22, No. 2 (2023) 22, No. 1 (2023) 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 17 Champneys, Alan R. 17 Kutz, J. Nathan 16 Uldall Kristiansen, K. 15 Rubin, Jonathan E. 14 Ward, Michael J. 13 Bressloff, Paul C. 13 Golubitsky, Martin A. 13 Guckenheimer, John M. 13 Ha, Seung-Yeal 13 Meiss, James D. 12 Mischaikow, Konstantin 12 Sandstede, Björn 11 Mireles-James, Jason D. 11 Rademacher, Jens Diederich Michael 11 Wechselberger, Martin 10 de la Llave, Rafael 10 Hogan, S. John 10 Lessard, Jean-Philippe 9 Bollt, Erik M. 9 Doelman, Arjen 9 Mezić, Igor 9 Porter, Mason Alexander 9 Scheel, Arnd 9 Wilson, Dan D. 8 Brunton, Steven L. 8 Ermentrout, Bard G. 8 Ermentrout, George Bard 8 Kilpatrick, Zachary P. 8 Kirk, Vivien 8 Knobloch, Edgar 8 Kolokolnikov, Theodore 8 Moehlis, Jeff 8 Pelinovsky, Dmitry Efimovich 8 Stewart, Ian Nicholas 8 Yorke, James Alan 7 Clément, Frédérique 7 Desroches, Mathieu 7 Gedeon, Tomáš 7 Holmes, Philip J. 7 Kevrekidis, Ioannis George 7 Kevrekidis, Panayotis G. 7 Kühn, Christian 7 Kuznetsov, Yuri Alexandrovich 7 Postlethwaite, Claire M. 7 Rucklidge, Alastair M. 7 Sieber, Jan 7 Zgliczyński, Piotr 6 Ashwin, Peter 6 Coombes, Stephen 6 Dullin, Holger R. 6 Kopell, Nancy J. 6 Lloyd, David J. B. 6 Mrozek, Marian 6 Palacián, Jesús F. 6 Starke, Jens 6 Terman, David Hillel 6 van den Berg, Jan Bouwe 6 Vidal, Claudio 6 Wilczak, Daniel 6 Yanchuk, Sergiĭ Volodymyrovych 6 Yanguas, Patricia 5 Avitabile, Daniele 5 Balasuriya, Sanjeeva 5 Cors, Josep Maria 5 Cummins, Bree 5 Fetecau, Razvan C. 5 Folias, Stefanos E. 5 Froyland, Gary 5 Giesl, Peter 5 Gottwald, Georg A. 5 Hüls, Thorsten 5 Hupkes, Hermen Jan 5 Jeffrey, Mike R. 5 Lee, Euiwoo 5 Lewis, Mark Alun 5 Lewis, Timothy J. 5 Rom-Kedar, Vered 5 Rotstein, Horacio G. 5 Rowley, Clarence Worth 5 Teixeira, Marco Antonio 5 Wanner, Thomas 5 Wayne, Clarence Eugene 5 Wulff, Claudia 4 Aguirre, Pablo 4 Atay, Fatihcan M. 4 Batko, Bogdan 4 Beck, Margaret 4 Bertram, Richard 4 Beyn, Wolf-Jürgen 4 Blömker, Dirk 4 Booth, Victoria 4 Bose, Amitabha 4 Buono, Pietro-Luciano 4 Capinski, Maciej J. 4 Cappelletti, Daniele 4 Chiba, Hayato 4 Chow, Carson C. 4 Colombo, Alessandro G. ...and 2,049 more Authors all top 5 Fields 757 Dynamical systems and ergodic theory (37-XX) 550 Ordinary differential equations (34-XX) 397 Biology and other natural sciences (92-XX) 311 Partial differential equations (35-XX) 186 Numerical analysis (65-XX) 172 Mechanics of particles and systems (70-XX) 84 Systems theory; control (93-XX) 82 Probability theory and stochastic processes (60-XX) 76 Fluid mechanics (76-XX) 45 Statistical mechanics, structure of matter (82-XX) 41 Computer science (68-XX) 37 Combinatorics (05-XX) 33 Operations research, mathematical programming (90-XX) 32 Mechanics of deformable solids (74-XX) 32 Optics, electromagnetic theory (78-XX) 31 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 28 Difference and functional equations (39-XX) 27 Statistics (62-XX) 23 Integral equations (45-XX) 22 Operator theory (47-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 18 Classical thermodynamics, heat transfer (80-XX) 18 Information and communication theory, circuits (94-XX) 14 Geophysics (86-XX) 9 Global analysis, analysis on manifolds (58-XX) 9 Quantum theory (81-XX) 8 Approximations and expansions (41-XX) 8 General topology (54-XX) 8 Algebraic topology (55-XX) 7 Convex and discrete geometry (52-XX) 7 Differential geometry (53-XX) 7 Manifolds and cell complexes (57-XX) 6 Group theory and generalizations (20-XX) 5 Functional analysis (46-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Algebraic geometry (14-XX) 4 Measure and integration (28-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-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 1,089 Publications have been cited 12,967 times in 8,170 Documents Cited by ▼ Year ▼ Basic reproduction numbers for reaction-diffusion epidemic models. Zbl 1259.35120 Wang, Wendi; Zhao, Xiao-Qiang 296 2012 Wave structure and nonlinear balances in a family of evolutionary PDEs. Zbl 1088.76531 Holm, Darryl D.; Staley, Martin F. 150 2003 Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032 Stewart, Ian; Golubitsky, Martin; Pivato, Marcus 132 2003 On the critical coupling for Kuramoto oscillators. Zbl 1242.34096 Dörfler, Florian; Bullo, Francesco 130 2011 Canonical discontinuous planar piecewise linear systems. Zbl 1242.34020 Freire, Emilio; Ponce, Enrique; Torres, Francisco 128 2012 Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030 Golubitsky, Martin; Stewart, Ian; Török, Andrei 124 2005 Existence and bifurcation of canards in \(\mathbb R^3\) in the case of a folded node. Zbl 1090.34047 Wechselberger, Martin 109 2005 Global synchronization of linearly hybrid coupled networks with time-varying delay. Zbl 1161.94011 Yu, Wenwu; Cao, Jinde; Lü, Jinhu 107 2008 Dynamic mode decomposition with control. Zbl 1334.65199 Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 97 2016 Sufficient conditions for fast switching synchronization in time-varying network topologies. Zbl 1145.37345 Stilwell, Daniel J.; Bollt, Erik M.; Roberson, D. Gray 90 2006 Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator. Zbl 1381.37096 Arbabi, Hassan; Mezić, Igor 89 2017 Spatiotemporal dynamics of the diffusive mussel-algae model near Turing-Hopf bifurcation. Zbl 1382.35035 Song, Yongli; Jiang, Heping; Liu, Quan-Xing; Yuan, Yuan 73 2017 A vaccination model for transmission dynamics of influenza. Zbl 1067.92051 Alexander, M. E.; Bowman, C.; Moghadas, S. M.; Summers, R.; Gumel, A. B.; Sahai, B. M. 66 2004 Nonlinear patterns in urban crime: hotspots, bifurcations, and suppression. Zbl 1282.91273 Short, M. B.; Bertozzi, A. L.; Brantingham, P. J. 65 2010 A primer of swarm equilibria. Zbl 1255.35012 Bernoff, Andrew J.; Topaz, Chad M. 64 2011 PDE methods for nonlocal models. Zbl 1088.34011 Laing, Carlo R.; Troy, William C. 63 2003 Mixed-mode oscillations in three time-scale systems: a prototypical example. Zbl 1167.34346 Krupa, Martin; Popović, Nikola; Kopell, Nancy 63 2008 Neuronal networks with gap junctions: a study of piecewise linear planar neuron models. Zbl 1159.92008 Coombes, S. 63 2008 On the implementation of the 0-1 test for chaos. Zbl 1161.37054 Gottwald, Georg A.; Melbourne, Ian 62 2009 Classification of asymptotic behavior in a stochastic SIR model. Zbl 1343.34109 Dieu, N. T.; Nguyen, D. H.; Du, N. H.; Yin, G. 62 2016 Random attractors for delay parabolic equations with additive noise and deterministic nonautonomous forcing. Zbl 1317.60081 Wang, Xiaohu; Lu, Kening; Wang, Bixiang 60 2015 Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. Zbl 1447.65119 Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M. 58 2020 Global phase-locking in finite populations of phase-coupled oscillators. Zbl 1167.34330 Verwoerd, Mark; Mason, Oliver 56 2008 Localized hexagon patterns of the planar Swift-Hohenberg equation. Zbl 1168.35311 Lloyd, David J. B.; Sandstede, Björn; Avitabile, Daniele; Champneys, Alan R. 56 2008 Evans functions for integral neural field equations with Heaviside firing rate function. Zbl 1067.92019 Coombes, S.; Owen, M. R. 56 2004 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025 Guckenheimer, John 55 2008 A database schema for the analysis of global dynamics of multiparameter systems. Zbl 1186.37021 Arai, Zin; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Pilarczyk, Paweł 54 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 1210.37062 Haro, A.; de la Llave, R. 53 2007 Projecting to a slow manifold: singularly perturbed systems and legacy codes. Zbl 1170.34343 Gear, C. W.; Kaper, T. J.; Kevrekidis, I. G.; Zagaris, A. 53 2005 Defects in oscillatory media: toward a classification. Zbl 1059.37062 Sandstede, Björn; Scheel, Arnd 53 2004 Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050 Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C. 52 2005 A geometric approach to the global attractor conjecture. Zbl 1301.34063 Gopalkrishnan, Manoj; Miller, Ezra; Shiu, Anne 51 2014 Multiresolution dynamic mode decomposition. Zbl 1338.37121 Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. 51 2016 Data-driven identification of parametric partial differential equations. Zbl 1456.65096 Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan 51 2019 \(R_0\) analysis of a spatiotemporal model for a stream population. Zbl 1252.35068 Mckenzie, H. W.; Jin, Y.; Jacobsen, J.; Lewis, M. A. 49 2012 Breathing pulses in an excitatory neural network. Zbl 1058.92010 Folias, Stefanos E.; Bressloff, Paul C. 49 2004 HJB-POD-based feedback design for the optimal control of evolution problems. Zbl 1058.35061 Kunisch, K.; Volkwein, S.; Xie, L. 49 2004 A discrete data assimilation scheme for the solutions of the two-dimensional Navier-Stokes equations and their statistics. Zbl 1362.35208 Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 49 2016 Power-law kinetics and determinant criteria for the preclusion of multistationarity in networks of interacting species. Zbl 1278.92012 Wiuf, Carsten; Feliu, Elisenda 49 2013 The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033 Chen, W.; Ward, M. J. 48 2011 A computational and geometric approach to phase resetting curves and surfaces. Zbl 1216.34030 Guillamon, Antoni; Huguet, Gemma 48 2009 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 48 2003 Higher order dynamic mode decomposition. Zbl 1373.37169 Le Clainche, Soledad; Vega, José M. 47 2017 Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters \(H\in(1/3,1/2]\). Zbl 1336.60103 Garrido-Atienza, María J.; Lu, Kening; Schmalfuss, Björn 47 2016 Nonsmooth Lagrangian mechanics and variational collision integrators. Zbl 1088.37045 Fetecau, R. C.; Marsden, J. E.; Ortiz, M.; West, M. 45 2003 Freezing solutions of equivariant evolution equations. Zbl 1061.65078 Beyn, W.-J.; Thümmler, V. 45 2004 Kink-antikink collisions in the \(\phi^4\) equation: the \(n\)-bounce resonance and the separatrix map. Zbl 1145.74370 Goodman, Roy H.; Haberman, Richard 44 2005 Complete entrainment of Lohe oscillators under attractive and repulsive couplings. Zbl 1310.34060 Choi, Sun-Ho; Ha, Seung-Yeal 44 2014 Nondeterministic chaos, and the two-fold singularity in piecewise smooth flows. Zbl 1227.34044 Colombo, Alessandro; Jeffrey, Mike R. 42 2011 Asymptotic dynamics of attractive-repulsive swarms. Zbl 1168.92045 Leverentz, Andrew J.; Topaz, Chad M.; Bernoff, Andrew J. 42 2009 On computing the critical coupling coefficient for the Kuramoto model on a complete bipartite graph. Zbl 1167.34331 Verwoerd, Mark; Mason, Oliver 41 2009 Linearly recurrent autoencoder networks for learning dynamics. Zbl 1489.65164 Otto, Samuel E.; Rowley, Clarence W. 41 2019 The two-fold singularity of discontinuous vector fields. Zbl 1178.34042 Jeffrey, M. R.; Colombo, A. 40 2009 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005 Guckenheimer, John; Oliva, Ricardo A. 40 2002 Uniform attractors for nonautonomous wave equations with nonlinear damping. Zbl 1210.35160 Sun, Chunyou; Cao, Daomin; Duan, Jinqiao 39 2007 Dynamics at a switching intersection: hierarchy, isonomy, and multiple sliding. Zbl 1310.34018 Jeffrey, Mike R. 39 2014 To snake or not to snake in the planar Swift-Hohenberg equation. Zbl 1200.37014 Avitabile, Daniele; Lloyd, David J. B.; Burke, John; Knobloch, Edgar; Sandstede, Björn 39 2010 Noise-induced behaviors in neural mean field dynamics. Zbl 1235.92016 Touboul, Jonathan; Hermann, Geoffroy; Faugeras, Olivier 38 2012 Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system. Zbl 1167.34361 Abaid, Nicole; Eisenberg, Robert S.; Liu, Weishi 38 2008 Stationary coexistence of hexagons and rolls via rigorous computations. Zbl 1371.37036 van den Berg, Jan Bouwe; Deschênes, Andréa; Lessard, Jean-Philippe; Mireles James, Jason D. 37 2015 Study of singularities in nonsmooth dynamical systems via singular perturbation. Zbl 1167.34304 Llibre, Jaume; Da Silva, Paulo R.; Teixeira, Marco A. 36 2009 Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. Zbl 1058.35050 Day, Sarah; Hiraoka, Yasuaki; Mischaikow, Konstantin; Ogawa, Toshiyuki 36 2005 Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. Zbl 1302.35386 Burger, Martin; Fetecau, Razvan; Huang, Yanghong 36 2014 Speeds of spread and propagation for KPP models in time almost and space periodic media. Zbl 1172.35423 Huang, Jianhua; Shen, Wenxian 36 2009 Parameterization of invariant manifolds for periodic orbits. I: Efficient numerics via the Floquet normal form. Zbl 1376.37057 Castelli, Roberto; Lessard, Jean-Philippe; Mireles James, J. D. 36 2015 Wandering bumps in stochastic neural fields. Zbl 1278.92007 Kilpatrick, Zachary P.; Ermentrout, Bard 36 2013 Bifurcations in delay differential equations and applications to tumor and immune system interaction models. Zbl 1284.34118 Bi, Ping; Ruan, Shigui 36 2013 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060 Guckenheimer, John; Kuehn, Christian 35 2010 Computation of mixed type functional differential boundary value problems. Zbl 1090.65093 Abell, Kate A.; Elmer, Christopher E.; Humphries, A. R.; Van Vleck, Erik S. 35 2005 Existence and stability of standing pulses in neural networks. I: Existence. Zbl 1109.34002 Guo, Yixin; Chow, Carson C. 34 2005 Continuation of quasi-periodic invariant tori. Zbl 1090.37057 Schilder, Frank; Osinga, Hinke M.; Vogt, Werner 34 2005 A collisionless singular Cucker-Smale model with decentralized formation control. Zbl 1432.34063 Choi, Young-Pil; Kalise, Dante; Peszek, Jan; Peters, Andrés A. 34 2019 Integration of dissipative partial differential equations: a case study. Zbl 1298.37071 Arioli, Gianni; Koch, Hans 34 2010 An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedbacks. Zbl 1210.34086 Xu, Jian; Chung, Kwok-Wai; Chan, Chuen-Lit 33 2007 Front propagation in stochastic neural fields. Zbl 1246.92004 Bressloff, Paul C.; Webber, Matthew A. 33 2012 Variable projection methods for an optimized dynamic mode decomposition. Zbl 1384.37122 Askham, Travis; Kutz, J. Nathan 33 2018 Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse. Zbl 1059.37067 England, J. P.; Krauskopf, B.; Osinga, H. M. 33 2004 \(R_0\) analysis of a benthic-drift model for a stream population. Zbl 1364.92059 Huang, Qihua; Jin, Yu; Lewis, Mark A. 33 2016 Dynamics of a time-delayed Lyme disease model with seasonality. Zbl 1365.35075 Wang, Xiunan; Zhao, Xiao-Qiang 33 2017 Local/global analysis of the stationary solutions of some neural field equations. Zbl 1194.92015 Veltz, Romain; Faugeras, Olivier 33 2010 Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. Zbl 1330.37029 Mireles James, J. D.; Mischaikow, Konstantin 33 2013 On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain. Zbl 1267.35027 Cvitanović, Predrag; Davidchack, Ruslan L.; Siminos, Evangelos 32 2010 Random attractor for damped nonlinear wave equations with white noise. Zbl 1094.35154 Zhou, Shengfan; Yin, Fuqi; Ouyang, Zigen 32 2005 The slow dynamics of two-spike solutions for the Gray-Scott and Gierer-Meinhardt systems: competition and oscillatory instabilities. Zbl 1145.35404 Sun, Wentao; Ward, Michael J.; Russell, Robert 32 2005 TC-HAT (\(\widehat{TC}\)): a novel toolbox for the continuation of periodic trajectories in hybrid dynamical systems. Zbl 1192.34004 Thota, Phanikrishna; Dankowicz, Harry 32 2008 Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model. Zbl 1167.34353 Rotstein, Horacio G.; Wechselberger, Martin; Kopell, Nancy 32 2008 Computing slow manifolds of saddle type. Zbl 1176.37026 Guckenheimer, John; Kuehn, Christian 32 2009 Semistrong pulse interactions in a class of coupled reaction-diffusion equations. Zbl 1088.35517 Doelman, Arjen; Kaper, Tasso J. 32 2003 An analytical approach to codimension-2 sliding bifurcations in the dry-friction oscillator. Zbl 1201.37086 Guardia, Marcel; Hogan, S. John; Seara, Tere M. 32 2010 The Melnikov method and subharmonic orbits in a piecewise-smooth system. Zbl 1262.37028 Granados, A.; Hogan, S. J.; Seara, T. M. 32 2012 Poisson-Nernst-Planck systems for ion flow with a local hard-sphere potential for ion size effects. Zbl 1284.34078 Lin, Guojian; Liu, Weishi; Yi, Yingfei; Zhang, Mingji 32 2013 Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108 Huguet, Gemma; de la Llave, Rafael 32 2013 The stability of a stripe for the Gierer-Meinhardt model and the effect of saturation. Zbl 1210.35016 Kolokolnikov, Theodore; Sun, Wentao; Ward, Michael; Wei, Juncheng 31 2006 Neural fields with distributed transmission speeds and long-range feedback delays. Zbl 1210.34118 Atay, Fatihcan M.; Hutt, Axel 31 2006 Some canonical bifurcations in the Swift-Hohenberg equation. Zbl 1210.34028 Peletier, L. A.; Williams, J. F. 31 2007 Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation. Zbl 1408.37062 van den Berg, Jan Bouwe; Lessard, Jean-Philippe 31 2008 A computational method to extract macroscopic variables and their dynamics in multiscale systems. Zbl 1320.37012 Froyland, Gary; Gottwald, Georg A.; Hammerlindl, Andy 31 2014 On the use of blowup to study regularizations of singularities of piecewise smooth dynamical systems in \(\mathbb{R}^3\). Zbl 1370.37100 Kristiansen, K. Uldall; Hogan, S. J. 31 2015 Homoclinic stripe patterns. Zbl 1004.35063 Doelman, Arjen; van der Ploeg, Harmen 31 2002 Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise. Zbl 1391.93265 de Wiljes, Jana; Reich, Sebastian; Stannat, Wilhelm 31 2018 Reaction network motifs for static and dynamic absolute concentration robustness. Zbl 1522.37091 Joshi, Badal; Craciun, Gheorghe 3 2023 An organizing center of codimension four in a predator-prey model with generalist predator: from tristability and quadristability to transients in a nonlinear environmental change. Zbl 1520.34046 Lu, Min; Huang, Jicai; Wang, Hao 3 2023 Stability analysis of the immune system induced by chemotaxis. Zbl 07741166 Zheng, Pan; Shan, Wenhai; Liao, Guangyuan 3 2023 Phase oscillator networks with nonlocal higher-order interactions: twisted states, stability, and bifurcations. Zbl 1523.35273 Bick, Christian; Böhle, Tobias; Kuehn, Christian 2 2023 Degenerate Turing bifurcation and the birth of localized patterns in activator-inhibitor systems. Zbl 07723356 Villar-Sepúlveda, Edgardo; Champneys, Alan 2 2023 Non-Markovian models of opinion dynamics on temporal networks. Zbl 1522.91185 Chu, Weiqi; Porter, Mason A. 2 2023 Continuation with noninvasive control schemes: revealing unstable states in a pedestrian evacuation scenario. Zbl 07674585 Panagiotopoulos, Ilias; Starke, Jens; Sieber, Jan; Just, Wolfram 2 2023 Resonances and phase locking phenomena for foliation preserving torus maps. Zbl 1515.37060 He, Xiaolong; de la Llave, Rafael 2 2023 Low-order parametric state-space modeling of MIMO systems in the Loewner framework. Zbl 07773362 Vojkovic, Tea; Quero, David; Poussot-Vassal, Charles; Vuillemin, Pierre 1 2023 Fast adjoint algorithm for linear responses of hyperbolic chaos. Zbl 07773370 Ni, Angxiu 1 2023 Learning to forecast dynamical systems from streaming data. Zbl 1522.37089 Giannakis, Dimitrios; Henriksen, Amelia; Tropp, Joel A.; Ward, Rachel 1 2023 A pulsed-precipitation model of dryland vegetation pattern formation. Zbl 1518.35071 Gandhi, Punit; Liu, Lily; Silber, Mary 1 2023 Mixed-mode oscillations in coupled Fitzhugh-Nagumo oscillators: blow-up analysis of cusped singularities. Zbl 1521.34058 Kristiansen, Kristian Uldall; Pedersen, Morten Gram 1 2023 On a finite-size neuronal population equation. Zbl 1515.60146 Schmutz, Valentin; Löcherbach, Eva; Schwalger, Tilo 1 2023 Decomposition of admissible functions in weighted coupled cell networks. Zbl 07712425 Sequeira, Pedro M.; Hespanha, João P.; Pedro Aguiar, A. 1 2023 Geometric singular perturbation analysis of the multiple-timescale Hodgkin-Huxley equations. Zbl 1522.34074 Kaklamanos, Panagiotis; Popović, Nikola; Kristiansen, Kristian U. 1 2023 Persistence of periodic orbits under state-dependent delayed perturbations: computer-assisted proofs. Zbl 1522.34094 Gimeno, Joan; Lessard, Jean-Philippe; Mireles James, J. D.; Yang, Jiaqi 1 2023 Fronts in the wake of a parameter ramp: slow passage through pitchfork and fold bifurcations. Zbl 07741159 Goh, Ryan; Kaper, Tasso J.; Scheel, Arnd; Vo, Theodore 1 2023 Extinction of multiple populations and a team of die-out Lyapunov functions. Zbl 1528.37073 Akhavan, Naghmeh; Yorke, James A. 1 2023 Hopf bifurcations of reaction networks with zero-one stoichiometric coefficients. Zbl 1522.92027 Tang, Xiaoxian; Wang, Kaizhang 1 2023 Order and disorder in a cyclically competitive ecological community. Zbl 1512.35062 Stiadle, Thomas I.; Bayliss, Alvin; Volpert, Vladimir A. 1 2023 Hyperdissipative Navier-Stokes equations driven by time-dependent forces: invariant manifolds. Zbl 07674591 Wang, Rong-Nian; Zhao, Jia-Cheng; Miranville, Alain 1 2023 On a competition-diffusion-advection system from river ecology: mathematical analysis and numerical study. Zbl 1484.35034 Yan, Xiao; Nie, Hua; Zhou, Peng 20 2022 Local and global existence for nonlocal multispecies advection-diffusion models. Zbl 1494.35002 Giunta, Valeria; Hillen, Thomas; Lewis, Mark; Potts, Jonathan R. 9 2022 Modeling multilane traffic with moving obstacles by nonlocal balance laws. Zbl 1497.35315 Bayen, Alexandre; Friedrich, Jan; Keimer, Alexander; Pflug, Lukas; Veeravalli, Tanya 8 2022 An adaptive phase-amplitude reduction framework without \(\mathcal{O}(\epsilon)\) constraints on inputs. Zbl 1490.34045 Wilson, Dan 6 2022 Emergent behaviors of rotation matrix flocks. Zbl 1513.70057 Fetecau, Razvan C.; Ha, Seung-Yeal; Park, Hansol 5 2022 A dynamical theory for singular stochastic delay differential equations. I: Linear equations and a multiplicative ergodic theorem on fields of Banach spaces. Zbl 1490.34103 Varzaneh, M. Ghani; Riedel, S.; Scheutzow, M. 5 2022 Efficient computation of linear response of chaotic attractors with one-dimensional unstable manifolds. Zbl 1497.37103 Chandramoorthy, Nisha; Wang, Qiqi 4 2022 A bounded-confidence model of opinion dynamics on hypergraphs. Zbl 1482.91163 Hickok, Abigail; Kureh, Yacoub; Brooks, Heather Z.; Feng, Michelle; Porter, Mason A. 4 2022 Graphop mean-field limits for Kuramoto-type models. Zbl 1483.35270 Gkogkas, Marios Antonios; Kuehn, Christian 4 2022 Limitations and improvements of the intelligent driver model (IDM). Zbl 1512.90062 Albeaik, Saleh; Bayen, Alexandre; Chiri, Maria Teresa; Gong, Xiaoqian; Hayat, Amaury; Kardous, Nicolas; Keimer, Alexander; McQuade, Sean T.; Piccoli, Benedetto; You, Yiling 4 2022 Derivative-free Bayesian inversion using multiscale dynamics. Zbl 1493.62132 Pavliotis, G. A.; Stuart, A. M.; Vaes, U. 4 2022 Persistence of Conley-Morse graphs in combinatorial dynamical systems. Zbl 1498.37069 Dey, Tamal K.; Mrozek, Marian; Slechta, Ryan 3 2022 Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock. Zbl 1509.34045 Castro, Sofia B. S. D.; Ferreira, Ana; Garrido-da-Silva, Liliana; Labouriau, Isabel S. 3 2022 Modulation and amplitude equations on bounded domains for nonlinear SPDEs driven by cylindrical \(\alpha\)-stable Lévy processes. Zbl 1492.60197 Yuan, Shenglan; Bloemker, Dirk 3 2022 Dynamics of small particle inertial migration in curved square ducts. 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Zbl 1501.34020 Kristiansen, Kristian U. 2 2021 Stability of motion induced by a point vortex under arbitrary polynomial perturbations. Zbl 1466.37046 Liu, Qihuai; Torres, Pedro J. 2 2021 Traveling pulse solutions in a three-component FitzHugh-Nagumo model. Zbl 1462.35038 Teramoto, Takashi; van Heijster, Peter 2 2021 ...and 989 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 10,175 Authors 100 Ha, Seung-Yeal 58 Llibre, Jaume 47 Krauskopf, Bernd 47 Kühn, Christian 47 Lessard, Jean-Philippe 45 Ward, Michael J. 42 Mireles-James, Jason D. 40 Osinga, Hinke Maria 39 Kevrekidis, Ioannis George 38 Kutz, J. Nathan 35 Bressloff, Paul C. 35 Sandstede, Björn 35 Scheel, Arnd 34 Brunton, Steven L. 32 Rubin, Jonathan E. 32 Stewart, Ian Nicholas 32 Wechselberger, Martin 31 Carrillo de la Plata, José Antonio 29 Kevrekidis, Panayotis G. 28 Craciun, Gheorghe 28 de la Llave, Rafael 28 Mezić, Igor 28 Novaes, Douglas Duarte 28 Park, Hansol 28 Wei, Juncheng 28 Zhao, Xiao-Qiang 27 Uldall Kristiansen, K. 26 Hupkes, Hermen Jan 26 Mischaikow, Konstantin 26 Pelinovsky, Dmitry Efimovich 26 Shen, Wenxian 26 Teixeira, Marco Antonio 25 Wang, Hao 24 Coombes, Stephen 24 Desroches, Mathieu 24 Kim, Dohyun 23 Kolokolnikov, Theodore 23 van den Berg, Jan Bouwe 23 Wang, Jinliang 22 Doelman, Arjen 22 Jeffrey, Mike R. 22 Laing, Carlo R. 22 Ponce, Enrique 22 van Heijster, Peter 21 Adimy, Mostafa 21 Ashwin, Peter 21 Simpson, David John Warwick 21 Wang, Bixiang 21 Wilson, Dan D. 20 Chen, Guanrong 20 de Carvalho, Tiago 20 Duan, Jinqiao 20 Fetecau, Razvan C. 20 Knobloch, Edgar 20 Moehlis, Jeff 20 Rademacher, Jens Diederich Michael 19 Balasuriya, Sanjeeva 19 Cao, Jinde 19 Dias, Ana Paula S. 19 Golubitsky, Martin A. 19 Kilpatrick, Zachary P. 19 Porfiri, Maurizio 19 Zgliczyński, Piotr 18 Blömker, Dirk 18 Bollt, Erik M. 18 Faye, Grégory 18 Sherratt, Jonathan A. 17 Aguiar, Manuela A. D. 17 Feliu, Elisenda 17 Gao, Hongjun 17 Gedeon, Tomáš 17 Ghosh, Dibakar 17 Lawley, Sean D. 17 Teng, Zhi-dong 17 Wanner, Thomas 17 Zhang, Mingji 17 Zhang, Xiang 16 Bi, Qinsheng 16 Cai, Yongli 16 Gardini, Laura 16 Huang, Lihong 16 Liu, Weishi 16 Meiss, James D. 16 Mrozek, Marian 16 Shi, Junping 16 Sieber, Jan 16 Song, Yongli 16 Wang, Weiming 16 Wyller, John A. 15 Bramburger, Jason J. 15 Froyland, Gary 15 Giannakis, Dimitrios 15 Kaper, Tasso J. 15 Li, Shimin 15 Li, Zhuchun 15 Park, Jinyeong 15 Tonon, Durval José 15 Wu, Jianhong 15 Xu, Jian 14 Alla, Alessandro ...and 10,075 more Authors all top 5 Cited in 530 Journals 517 SIAM Journal on Applied Dynamical Systems 420 Physica D 321 Journal of Differential Equations 306 Chaos 292 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 217 Discrete and Continuous Dynamical Systems. 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A 21 Journal of Scientific Computing 21 International Journal of Robust and Nonlinear Control 21 SIAM/ASA Journal on Uncertainty Quantification 20 Japan Journal of Industrial and Applied Mathematics 20 Journal of Mathematical Chemistry 19 Kinetic and Related Models 18 Neural Networks 17 Numerische Mathematik 17 Advances in Computational Mathematics 16 Inverse Problems 16 Transactions of the American Mathematical Society 16 Applied Numerical Mathematics 16 Complexity 16 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 15 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 15 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 Journal of Statistical Mechanics: Theory and Experiment 14 Ergodic Theory and Dynamical Systems 14 Discrete Dynamics in Nature and Society 14 Foundations of Computational Mathematics 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis ...and 430 more Journals all top 5 Cited in 61 Fields 2,568 Biology and other natural sciences (92-XX) 2,485 Dynamical systems and ergodic theory (37-XX) 2,479 Partial differential equations (35-XX) 2,478 Ordinary differential equations (34-XX) 976 Numerical analysis (65-XX) 740 Systems theory; control (93-XX) 611 Mechanics of particles and systems (70-XX) 572 Fluid mechanics (76-XX) 537 Probability theory and stochastic processes (60-XX) 313 Statistical mechanics, structure of matter (82-XX) 264 Computer science (68-XX) 214 Calculus of variations and optimal control; optimization (49-XX) 211 Mechanics of deformable solids (74-XX) 206 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 176 Statistics (62-XX) 174 Operations research, mathematical programming (90-XX) 160 Operator theory (47-XX) 144 Combinatorics (05-XX) 133 Integral equations (45-XX) 132 Difference and functional equations (39-XX) 114 Information and communication theory, circuits (94-XX) 106 Quantum theory (81-XX) 98 Optics, electromagnetic theory (78-XX) 86 Classical thermodynamics, heat transfer (80-XX) 73 Global analysis, analysis on manifolds (58-XX) 70 Geophysics (86-XX) 68 Differential geometry (53-XX) 56 Real functions (26-XX) 49 Linear and multilinear algebra; matrix theory (15-XX) 30 Approximations and expansions (41-XX) 28 Algebraic topology (55-XX) 24 Algebraic geometry (14-XX) 22 General and overarching topics; collections (00-XX) 22 Commutative algebra (13-XX) 22 Functional analysis (46-XX) 19 Harmonic analysis on Euclidean spaces (42-XX) 19 Convex and discrete geometry (52-XX) 17 Measure and integration (28-XX) 17 Special functions (33-XX) 17 Relativity and gravitational theory (83-XX) 16 Astronomy and astrophysics (85-XX) 15 Manifolds and cell complexes (57-XX) 14 General topology (54-XX) 13 Order, lattices, ordered algebraic structures (06-XX) 11 Field theory and polynomials (12-XX) 11 Group theory and generalizations (20-XX) 7 Topological groups, Lie groups (22-XX) 6 Number theory (11-XX) 6 Functions of a complex variable (30-XX) 5 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 5 Potential theory (31-XX) 5 Several complex variables and analytic spaces (32-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geometry (51-XX) 2 Associative rings and algebras (16-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 Mathematics education (97-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) Citations by Year