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: 1,149 Publications (since 2002) References Indexed: 598 Publications with 25,384 References. all top 5 Latest Issues 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 14 Ward, Michael J. 13 Bressloff, Paul C. 13 Champneys, Alan R. 13 Guckenheimer, John M. 13 Kutz, J. Nathan 13 Rubin, Jonathan E. 13 Uldall Kristiansen, K. 12 Golubitsky, Martin A. 12 Meiss, James D. 11 Wechselberger, Martin 10 Ha, Seung-Yeal 10 Mischaikow, Konstantin 10 Rademacher, Jens Diederich Michael 10 Sandstede, Björn 9 de la Llave, Rafael 9 Doelman, Arjen 9 Mireles-James, Jason D. 8 Bollt, Erik M. 8 Brunton, Steven L. 8 Hogan, S. John 8 Kirk, Vivien 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 Knobloch, Edgar 7 Mezić, Igor 7 Pelinovsky, Dmitry Efimovich 7 Porter, Mason Alexander 7 Postlethwaite, Claire M. 7 Wilson, Dan D. 7 Zgliczyński, Piotr 6 Ashwin, Peter 6 Clément, Frédérique 6 Coombes, Stephen 6 Dullin, Holger R. 6 Gedeon, Tomáš 6 Kopell, Nancy J. 6 Kühn, Christian 6 Palacián, Jesús F. 6 Scheel, Arnd 6 Stewart, Ian Nicholas 6 van den Berg, Jan Bouwe 6 Wilczak, Daniel 6 Yanguas, Patricia 6 Yorke, James Alan 5 Avitabile, Daniele 5 Colombo, Alessandro G. 5 Folias, Stefanos E. 5 Gottwald, Georg A. 5 Kuznetsov, Yuri Alexandrovich 5 Lloyd, David J. B. 5 Mrozek, Marian 5 Rotstein, Horacio G. 5 Rowley, Clarence W. 5 Rucklidge, Alastair M. 5 Sieber, Jan 5 Wanner, Thomas 5 Wayne, Clarence Eugene 5 Wulff, Claudia 5 Yanchuk, Sergiĭ Volodymyrovych 4 Atay, Fatihcan M. 4 Balasuriya, Sanjeeva 4 Beck, Margaret 4 Bose, Amitabha 4 Buono, Pietro-Luciano 4 Capinski, Maciej J. 4 Chow, Carson C. 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 Dias, Ana Paula S. 4 Faye, Grégory 4 Fetecau, Razvan C. 4 Froyland, Gary 4 Giesl, Peter 4 Hupkes, Hermen Jan 4 Jeffrey, Mike R. 4 Keener, James P. 4 Laing, Carlo R. 4 Lewis, Timothy J. 4 Li, Zhuchun 4 MacLaurin, James N. 4 Neuberger, John M. 4 Oldeman, Bart E. 4 Porfiri, Maurizio 4 Roberts, Anthony John 4 Rom-Kedar, Vered 4 Sepulchre, Rodolphe J. 4 Sieben, Nándor ...and 1,720 more Authors all top 5 Fields 669 Dynamical systems and ergodic theory (37-XX) 497 Ordinary differential equations (34-XX) 336 Biology and other natural sciences (92-XX) 270 Partial differential equations (35-XX) 167 Numerical analysis (65-XX) 148 Mechanics of particles and systems (70-XX) 69 Fluid mechanics (76-XX) 67 Systems theory; control (93-XX) 64 Probability theory and stochastic processes (60-XX) 39 Statistical mechanics, structure of matter (82-XX) 32 Mechanics of deformable solids (74-XX) 31 Optics, electromagnetic theory (78-XX) 27 Computer science (68-XX) 25 Combinatorics (05-XX) 25 Operations research, mathematical programming (90-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Difference and functional equations (39-XX) 22 Integral equations (45-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 20 Operator theory (47-XX) 20 Statistics (62-XX) 18 Classical thermodynamics, heat transfer (80-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 12 Geophysics (86-XX) 12 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 Algebraic topology (55-XX) 6 Manifolds and cell complexes (57-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Group theory and generalizations (20-XX) 5 Approximations and expansions (41-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Algebraic geometry (14-XX) 3 Measure and integration (28-XX) 3 Functional analysis (46-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Mathematical logic and foundations (03-XX) 1 Real functions (26-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 957 Publications have been cited 9,808 times in 6,238 Documents Cited by ▼ Year ▼ Basic reproduction numbers for reaction-diffusion epidemic models. Zbl 1259.35120Wang, Wendi; Zhao, Xiao-Qiang 184 2012 Wave structure and nonlinear balances in a family of evolutionary PDEs. Zbl 1088.76531Holm, Darryl D.; Staley, Martin F. 127 2003 Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032Stewart, Ian; Golubitsky, Martin; Pivato, Marcus 113 2003 Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030Golubitsky, Martin; Stewart, Ian; Török, Andrei 111 2005 On the critical coupling for Kuramoto oscillators. Zbl 1242.34096Dörfler, Florian; Bullo, Francesco 108 2011 Global synchronization of linearly hybrid coupled networks with time-varying delay. Zbl 1161.94011Yu, Wenwu; Cao, Jinde; Lü, Jinhu 99 2008 Canonical discontinuous planar piecewise linear systems. Zbl 1242.34020Freire, Emilio; Ponce, Enrique; Torres, Francisco 95 2012 Existence and bifurcation of canards in \(\mathbb R^3\) in the case of a folded node. Zbl 1090.34047Wechselberger, Martin 92 2005 Sufficient conditions for fast switching synchronization in time-varying network topologies. Zbl 1145.37345Stilwell, Daniel J.; Bollt, Erik M.; Roberson, D. Gray 79 2006 Dynamic mode decomposition with control. Zbl 1334.65199Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 64 2016 PDE methods for nonlocal models. Zbl 1088.34011Laing, Carlo R.; Troy, William C. 58 2003 Neuronal networks with gap junctions: a study of piecewise linear planar neuron models. Zbl 1159.92008Coombes, S. 57 2008 A primer of swarm equilibria. Zbl 1255.35012Bernoff, Andrew J.; Topaz, Chad M. 54 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. 53 2004 Global phase-locking in finite populations of phase-coupled oscillators. Zbl 1167.34330Verwoerd, Mark; Mason, Oliver 52 2008 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 Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C. 49 2005 Evans functions for integral neural field equations with Heaviside firing rate function. Zbl 1067.92019Coombes, S.; Owen, M. R. 49 2004 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025Guckenheimer, John 48 2008 On the implementation of the 0-1 test for chaos. Zbl 1161.37054Gottwald, Georg A.; Melbourne, Ian 47 2009 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 47 2009 Spatiotemporal dynamics of the diffusive mussel-algae model near Turing-Hopf bifurcation. Zbl 1382.35035Song, Yongli; Jiang, Heping; Liu, Quan-Xing; Yuan, Yuan 46 2017 Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator. Zbl 1381.37096Arbabi, Hassan; Mezić, Igor 46 2017 Localized hexagon patterns of the planar Swift-Hohenberg equation. Zbl 1168.35311Lloyd, David J. B.; Sandstede, Björn; Avitabile, Daniele; Champneys, Alan R. 46 2008 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. 45 2007 Mixed-mode oscillations in three time-scale systems: a prototypical example. Zbl 1167.34346Krupa, Martin; Popović, Nikola; Kopell, Nancy 45 2008 Defects in oscillatory media: toward a classification. Zbl 1059.37062Sandstede, Björn; Scheel, Arnd 45 2004 Breathing pulses in an excitatory neural network. Zbl 1058.92010Folias, Stefanos E.; Bressloff, Paul C. 44 2004 Nonlinear patterns in urban crime: hotspots, bifurcations, and suppression. Zbl 1282.91273Short, M. B.; Bertozzi, A. L.; Brantingham, P. J. 44 2010 A computational and geometric approach to phase resetting curves and surfaces. Zbl 1216.34030Guillamon, Antoni; Huguet, Gemma 42 2009 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 41 2003 A geometric approach to the global attractor conjecture. Zbl 1301.34063Gopalkrishnan, Manoj; Miller, Ezra; Shiu, Anne 40 2014 HJB-POD-based feedback design for the optimal control of evolution problems. Zbl 1058.35061Kunisch, K.; Volkwein, S.; Xie, L. 39 2004 Classification of asymptotic behavior in a stochastic SIR model. Zbl 1343.34109Dieu, N. T.; Nguyen, D. H.; Du, N. H.; Yin, G. 38 2016 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005Guckenheimer, John; Oliva, Ricardo A. 37 2002 On computing the critical coupling coefficient for the Kuramoto model on a complete bipartite graph. Zbl 1167.34331Verwoerd, Mark; Mason, Oliver 37 2009 Asymptotic dynamics of attractive-repulsive swarms. Zbl 1168.92045Leverentz, Andrew J.; Topaz, Chad M.; Bernoff, Andrew J. 37 2009 Freezing solutions of equivariant evolution equations. Zbl 1061.65078Beyn, W.-J.; Thümmler, V. 37 2004 \(R_0\) analysis of a spatiotemporal model for a stream population. Zbl 1252.35068Mckenzie, H. W.; Jin, Y.; Jacobsen, J.; Lewis, M. A. 37 2012 Multiresolution dynamic mode decomposition. Zbl 1338.37121Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. 37 2016 Nondeterministic chaos, and the two-fold singularity in piecewise smooth flows. Zbl 1227.34044Colombo, Alessandro; Jeffrey, Mike R. 36 2011 The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033Chen, W.; Ward, M. J. 36 2011 Nonsmooth Lagrangian mechanics and variational collision integrators. Zbl 1088.37045Fetecau, R. C.; Marsden, J. E.; Ortiz, M.; West, M. 36 2003 The two-fold singularity of discontinuous vector fields. Zbl 1178.34042Jeffrey, M. R.; Colombo, A. 35 2009 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. 35 2016 Noise-induced behaviors in neural mean field dynamics. Zbl 1235.92016Touboul, Jonathan; Hermann, Geoffroy; Faugeras, Olivier 34 2012 Computation of mixed type functional differential boundary value problems. Zbl 1090.65093Abell, Kate A.; Elmer, Christopher E.; Humphries, A. R.; Van Vleck, Erik S. 34 2005 Complete entrainment of Lohe oscillators under attractive and repulsive couplings. Zbl 1310.34060Choi, Sun-Ho; Ha, Seung-Yeal 33 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 33 2010 Study of singularities in nonsmooth dynamical systems via singular perturbation. Zbl 1167.34304Llibre, Jaume; Da Silva, Paulo R.; Teixeira, Marco A. 32 2009 Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. Zbl 1058.35050Day, Sarah; Hiraoka, Yasuaki; Mischaikow, Konstantin; Ogawa, Toshiyuki 32 2005 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. 32 2015 Dynamics at a switching intersection: hierarchy, isonomy, and multiple sliding. Zbl 1310.34018Jeffrey, Mike R. 31 2014 Existence and stability of standing pulses in neural networks. I: Existence. Zbl 1109.34002Guo, Yixin; Chow, Carson C. 31 2005 Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. Zbl 1330.37029Mireles James, J. D.; Mischaikow, Konstantin 31 2013 Integration of dissipative partial differential equations: a case study. Zbl 1298.37071Arioli, Gianni; Koch, Hans 31 2010 Front propagation in stochastic neural fields. Zbl 1246.92004Bressloff, Paul C.; Webber, Matthew A. 31 2012 Random attractors for delay parabolic equations with additive noise and deterministic nonautonomous forcing. Zbl 1317.60081Wang, Xiaohu; Lu, Kening; Wang, Bixiang 31 2015 Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. Zbl 1302.35386Burger, Martin; Fetecau, Razvan; Huang, Yanghong 31 2014 Homoclinic stripe patterns. Zbl 1004.35063Doelman, Arjen; van der Ploeg, Harmen 30 2002 Power-law kinetics and determinant criteria for the preclusion of multistationarity in networks of interacting species. Zbl 1278.92012Wiuf, Carsten; Feliu, Elisenda 30 2013 Bifurcations in delay differential equations and applications to tumor and immune system interaction models. Zbl 1284.34118Bi, Ping; Ruan, Shigui 30 2013 Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system. Zbl 1167.34361Abaid, Nicole; Eisenberg, Robert S.; Liu, Weishi 30 2008 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 29 2007 Semistrong pulse interactions in a class of coupled reaction-diffusion equations. Zbl 1088.35517Doelman, Arjen; Kaper, Tasso J. 29 2003 Continuation of quasi-periodic invariant tori. Zbl 1090.37057Schilder, Frank; Osinga, Hinke M.; Vogt, Werner 29 2005 Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108Huguet, Gemma; de la Llave, Rafael 29 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 Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model. Zbl 1167.34353Rotstein, Horacio G.; Wechselberger, Martin; Kopell, Nancy 29 2008 Speeds of spread and propagation for KPP models in time almost and space periodic media. Zbl 1172.35423Huang, Jianhua; Shen, Wenxian 29 2009 Computing slow manifolds of saddle type. Zbl 1176.37026Guckenheimer, John; Kuehn, Christian 29 2009 Local/global analysis of the stationary solutions of some neural field equations. Zbl 1194.92015Veltz, Romain; Faugeras, Olivier 29 2010 Neural fields with distributed transmission speeds and long-range feedback delays. Zbl 1210.34118Atay, Fatihcan M.; Hutt, Axel 28 2006 Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart 28 2007 Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation. Zbl 1408.37062van den Berg, Jan Bouwe; Lessard, Jean-Philippe 28 2008 Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse. Zbl 1059.37067England, J. P.; Krauskopf, B.; Osinga, H. M. 28 2004 An analytical approach to codimension-2 sliding bifurcations in the dry-friction oscillator. Zbl 1201.37086Guardia, Marcel; Hogan, S. John; Seara, Tere M. 28 2010 Some canonical bifurcations in the Swift-Hohenberg equation. Zbl 1210.34028Peletier, L. A.; Williams, J. F. 27 2007 Uniform attractors for nonautonomous wave equations with nonlinear damping. Zbl 1210.35160Sun, Chunyou; Cao, Daomin; Duan, Jinqiao 27 2007 Kink-antikink collisions in the \(\phi^4\) equation: the \(n\)-bounce resonance and the separatrix map. Zbl 1145.74370Goodman, Roy H.; Haberman, Richard 27 2005 A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems. Zbl 1059.37068Day, S.; Junge, O.; Mischaikow, K. 27 2004 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. 27 2015 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. 27 2015 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 26 2006 Random attractor for damped nonlinear wave equations with white noise. Zbl 1094.35154Zhou, Shengfan; Yin, Fuqi; Ouyang, Zigen 26 2005 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060Guckenheimer, John; Kuehn, Christian 26 2010 The structure of MESSI biological systems. Zbl 1395.92071Pérez Millán, Mercedes; Dickenstein, Alicia 25 2018 Continuation-based computation of global isochrons. Zbl 1232.37014Osinga, Hinke M.; Moehlis, Jeff 25 2010 Wandering bumps in stochastic neural fields. Zbl 1278.92007Kilpatrick, Zachary P.; Ermentrout, Bard 25 2013 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 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 25 2016 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 24 2014 Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system. Zbl 1213.37046Wilczak, Daniel 24 2010 Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster. Zbl 1263.37036Linaro, Daniele; Champneys, Alan; Desroches, Mathieu; Storace, Marco 24 2012 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 24 2003 Reliable computation of robust response tori on the verge of breakdown. Zbl 1253.37077Figueras, Jordi-Lluís; Haro, Àlex 24 2012 Data-driven identification of parametric partial differential equations. Zbl 1456.65096Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan 23 2019 Scaling in singular perturbation problems: blowing up a relaxation oscillator. Zbl 1243.34066Kosiuk, Ilona; Szmolyan, Peter 23 2011 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 23 2013 Front interactions in a three-component system. Zbl 1197.35047van Heijster, P.; Doelman, A.; Kaper, T. J.; Promislow, K. 23 2010 On a competition-diffusion-advection system from river ecology: mathematical analysis and numerical study. Zbl 07484039Yan, Xiao; Nie, Hua; Zhou, Peng 3 2022 A dynamical theory for singular stochastic delay differential equations. I: Linear equations and a multiplicative ergodic theorem on fields of Banach spaces. Zbl 07484043Varzaneh, M. Ghani; Riedel, S.; Scheutzow, M. 2 2022 Rigorous verification of Hopf bifurcations via desingularization and continuation. Zbl 1476.37094van den Berg, Jan Bouwe; Lessard, Jean-Philippe; Queirolo, Elena 4 2021 A simple proof of asymptotic consensus in the Hegselmann-Krause and Cucker-Smale models with normalization and delay. Zbl 1466.34073Haskovec, Jan 4 2021 Symbolic proof of bistability in reaction networks. Zbl 1465.37105Torres, Angélica; Feliu, Elisenda 3 2021 High-order approximation of heteroclinic bifurcations in truncated 2D-normal forms for the generic cases of Hopf-zero and nonresonant double Hopf singularities. Zbl 1478.34067Qin, B. W.; Chung, K. W.; Algaba, A.; Rodríguez-Luis, A. J. 3 2021 Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation. Zbl 1482.34047Wang, Yangyang; Gill, Jeffrey P.; Chiel, Hillel J.; Thomas, Peter J. 2 2021 The pair-replica-mean-field limit for intensity-based neural networks. Zbl 1465.37064Baccelli, François; Taillefumier, Thibaud 2 2021 Pseudospectral approximation of Hopf bifurcation for delay differential equations. Zbl 1470.34185de Wolff, B. A. J.; Scarabel, F.; Verduyn Lunel, S. M.; Diekmann, O. 2 2021 Synchrony and oscillatory dynamics for a 2-d PDE-ODE model of diffusion-mediated communication between small signaling compartments. Zbl 1462.35227Iyaniwura, Sarafa A.; Ward, Michael J. 2 2021 High-frequency instabilities of the Kawahara equation: a perturbative approach. Zbl 1478.35072Creedon, Ryan; Deconinck, Bernard; Trichtchenko, Olga 2 2021 Nanoptera in weakly nonlinear woodpile chains and diatomic granular chains. Zbl 07444704Deng, Guo; Lustri, Christopher J.; Porter, Mason A. 2 2021 How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks. Zbl 1472.92137Grundel, Sara M.; Heyder, Stefan; Hotz, Thomas; Ritschel, Tobias K. S.; Sauerteig, Philipp; Worthmann, Karl 1 2021 The role of multiple repetitions on the size of a rumor. Zbl 1478.60268Rada, Alejandra; Coletti, Cristian; Lebensztayn, Elcio; Rodriguez, Pablo M. 1 2021 High-order accuracy computation of coupling functions for strongly coupled oscillators. Zbl 1472.92051Park, Youngmin; Wilson, Dan D. 1 2021 Abundance of strange attractors near an attracting periodically perturbed network. Zbl 1476.37059Rodrigues, Alexandre A. P. 1 2021 Dynamic transitions and bifurcations for a class of axisymmetric geophysical fluid flow. Zbl 1461.76172Han, Daozhi; Hernandez, Marco; Wang, Quan 1 2021 Stability of motion induced by a point vortex under arbitrary polynomial perturbations. Zbl 1466.37046Liu, Qihuai; Torres, Pedro J. 1 2021 Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics. Zbl 1468.34053Longo, Iacopo P.; Núñez, Carmen; Obaya, Rafael; Rasmussen, Martin 1 2021 Nonlinear consensus on networks: equilibria, effective resistance, and trees of motifs. Zbl 1478.05142Homs-Dones, Marc; Devriendt, Karel; Lambiotte, Renaud 1 2021 Optimal control of oscillation timing and entrainment using large magnitude inputs: an adaptive phase-amplitude-coordinate-based approach. Zbl 1475.92021Wilson, Dan 1 2021 Data assimilation for the Navier-Stokes equations using local observables. Zbl 1480.35309Biswas, Animikh; Bradshaw, Zachary; Jolly, Michael S. 1 2021 A stiction oscillator under slowly varying forcing: uncovering small scale phenomena using blowup. Zbl 07444702Kristiansen, Kristian U. 1 2021 Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. Zbl 1447.65119Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M. 20 2020 From the Lohe tensor model to the Lohe Hermitian sphere model and emergent dynamics. Zbl 1441.82011Ha, Seung-Yeal; Park, Hansol 8 2020 Physics-informed probabilistic learning of linear embeddings of nonlinear dynamics with guaranteed stability. Zbl 1442.37090Pan, Shaowu; Duraisamy, Karthik 8 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. 7 2020 Intralayer synchronization in evolving multiplex hypernetworks: analytical approach. Zbl 1441.37093Rakshit, Sarbendu; Bera, Bidesh K.; Bollt, Erik M.; Ghosh, Dibakar 7 2020 Mathematical modeling for schistosomiasis with seasonal influence: a case study in Hubei, China. Zbl 1445.37074Zhang, Tailei; Zhao, Xiao-Qiang 6 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 6 2020 Permanence of weakly reversible mass-action systems with a single linkage class. Zbl 1443.92110Boros, Balázs; Hofbauer, Josef 6 2020 Affine invariant interacting Langevin dynamics for Bayesian inference. Zbl 1472.65118Garbuno-Inigo, Alfredo; Nüsken, Nikolas; Reich, Sebastian 6 2020 Clamping and synchronization in the strongly coupled FitzHugh-Nagumo model. Zbl 1447.35335Quininao, Cristobal; Touboul, Jonathan D. 5 2020 Time-delay observables for Koopman: theory and applications. Zbl 1441.37090Kamb, Mason; Kaiser, Eurika; Brunton, Steven L.; Kutz, J. Nathan 5 2020 LOR for analysis of periodic dynamics: a one-stop shop approach. Zbl 1461.34065Letson, Benjamin; Rubin, Jonathan E. 4 2020 Computational singular perturbation method for nonstandard slow-fast systems. Zbl 1457.37102Lizarraga, Ian; Wechselberger, Martin 4 2020 Data-driven model predictive control using interpolated Koopman generators. Zbl 1461.49007Peitz, Sebastian; Otto, Samuel E.; Rowley, Clarence W. 4 2020 Barriers to the transport of diffusive scalars in compressible flows. Zbl 1448.76146Haller, George; Karrasch, Daniel; Kogelbauer, Florian 3 2020 Data based reconstruction of duplex networks. Zbl 1437.37123Ma, Chuang; Chen, Han-Shuang; Li, Xiang; Lai, Ying-Cheng; Zhang, Hai-Feng 3 2020 Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear flow. Zbl 1475.37094Lakshmi, Mayur V.; Fantuzzi, Giovanni; Fernández-Caballero, Jesús D.; Hwang, Yongyun; Chernyshenko, Sergei I. 3 2020 Bifurcations on fully inhomogeneous networks. Zbl 1443.34039Gandhi, Punit; Golubitsky, Martin; Postlethwaite, Claire; Stewart, Ian; Wang, Yangyang 3 2020 On the Koopman operator of algorithms. Zbl 1437.47048Dietrich, Felix; Thiem, Thomas N.; Kevrekidis, Ioannis G. 3 2020 Endotactic networks and toric differential inclusions. Zbl 1461.37077Craciun, Gheorghe; Deshpande, Abhishek 3 2020 Centering data improves the dynamic mode decomposition. Zbl 1465.37092Hirsh, Seth M.; Harris, Kameron Decker; Kutz, J. Nathan; Brunton, Bingni W. 3 2020 Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations. Zbl 1443.35072Alfaro, Matthieu; Ducrot, Arnaud; Faye, Grégory 2 2020 Alternative reduction by stages of Keplerian systems. Positive, negative, and zero energy. Zbl 1473.70027Crespo, Francisco; Ferrer, Sebastián 2 2020 Clusters tend to be of equal size in a negative feedback population model of cell cycle dynamics. Zbl 1447.37083Rombouts, Jan; Prathom, Kiattisak; Young, Todd R. 2 2020 Pulse solutions for an extended Klausmeier model with spatially varying coefficients. Zbl 1431.35071Bastiaansen, Robbin; Chirilus-Bruckner, Martina; Doelman, Arjen 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 Emergent behaviors of the Kuramoto model with a time delay on a general digraph. Zbl 07175470Dong, Jiu-Gang; Ha, Seung-Yeal; Kim, Doheon 2 2020 Conley index approach to sampled dynamics. Zbl 1442.37088Batko, Bogdan; Mischaikow, Konstantin; Mrozek, Marian; Przybylski, Mateusz 2 2020 Lotka-Volterra competition model on graphs. Zbl 1437.92103Slavík, Antonín 2 2020 Invariant synchrony subspaces of sets of matrices. Zbl 1442.15045Neuberger, John M.; Sieben, Nándor; Swift, James W. 2 2020 Hubs-attracting Laplacian and related synchronization on networks. Zbl 1439.05210Gambuzza, Lucia Valentina; Frasca, Mattia; Estrada, Ernesto 2 2020 Big ducks in the heart: canard analysis can explain large early afterdepolarizations in cardiomyocytes. Zbl 1460.92052Kimrey, Joshua; Vo, Theodore; Bertram, Richard 2 2020 Probabilistic foundations of spatial mean-field models in ecology and applications. Zbl 1466.60050Patterson, Denis D.; Levin, Simon A.; Staver, Carla; Touboul, Jonathan D. 2 2020 Tipping phenomena and points of no return in ecosystems: beyond classical bifurcations. Zbl 1467.37091O’Keeffe, Paul E.; Wieczorek, Sebastian 2 2020 Rate-induced tipping in discrete-time dynamical systems. Zbl 1445.37016Kiers, Claire 1 2020 Emergence of bicluster aggregation for the swarm sphere model with attractive-repulsive couplings. Zbl 1447.82022Ha, Seung-Yeal; Kim, Dohyun; Lee, Jaeseung; Noh, Se Eun 1 2020 On the stability of symmetric periodic orbits of the elliptic Sitnikov problem. Zbl 1476.70015Cen, Xiuli; Cheng, Xuhua; Huang, Zaitang; Zhang, Meirong 1 2020 Understanding mass transfer directions via data-driven models with application to mobile phone data. Zbl 1448.76028Alla, Alessandro; Balzotti, Caterina; Briani, Maya; Cristiani, Emiliano 1 2020 Finding strategies to regulate propagation and containment of dengue via invariant manifold analysis. Zbl 1445.37063Contreras-Julio, Dana; Aguirre, Pablo; Mujica, José; Vasilieva, Olga 1 2020 Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a twofold cycle. Zbl 1459.34059Novaes, Douglas D.; Seara, Tere M.; Teixeira, Marco A.; Zeli, Iris O. 1 2020 Phase reduction of stochastic biochemical oscillators. Zbl 1433.92015Bressloff, Paul C.; MacLaurin, James N. 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 Computing invariant sets of random differential equations using polynomial chaos. Zbl 1441.37057Breden, Maxime; Kuehn, Christian 1 2020 Invariant sets in quasiperiodically forced dynamical systems. Zbl 1442.37012Susuki, Yoshihiko; Mezić, Igor 1 2020 Elliptic bubbles in Moser’s 4D quadratic map: the quadfurcation. Zbl 1444.37046Bäcker, Arnd; Meiss, James D. 1 2020 Ribosome flow model with different site sizes. Zbl 1441.92020Bar-Shalom, Eyal; Ovseevich, Alexander; Margaliot, Michael 1 2020 State-dependent dynamics of the Lohe matrix ensemble on the unitary group under the gradient flow. Zbl 1443.34035Kim, Dohyun 1 2020 Stability in a Hebbian network of Kuramoto oscillators with second-order couplings for binary pattern retrieve. Zbl 1454.34083Zhao, Xiaoxue; Li, Zhuchun; Xue, Xiaoping 1 2020 Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration. Zbl 1468.37058Froyland, Gary; Koltai, Péter; Stahn, Martin 1 2020 Global time-renormalization of the gravitational \(N\)-body problem. Zbl 1476.70033Antoñana, Mikel; Chartier, Philippe; Makazaga, Joseba; Murua, Ander 1 2020 Koopman analysis of isolated fronts and solitons. Zbl 1465.37097Parker, Jeremy P.; Page, Jacob 1 2020 Bounding extreme events in nonlinear dynamics using convex optimization. Zbl 1461.93202Fantuzzi, Giovanni; Goluskin, David 1 2020 Effects of large permanent charges on ionic flows via Poisson-Nernst-Planck models. Zbl 1464.78003Zhang, Liwei; Liu, Weishi 1 2020 Weakly nonlinear analysis of peanut-shaped deformations for localized spots of singularly perturbed reaction-diffusion systems. Zbl 1472.35026Wong, Tony; Ward, Michael J. 1 2020 On the pitchfork bifurcation of the folded node and other unbounded time-reversible connection problems in \(\mathbb{R}^3\). Zbl 1470.37074Kristiansen, Kristian U. 1 2020 Stoker’s problem for quasi-periodically forced reversible systems with multidimensional Liouvillean frequency. Zbl 1470.70026Xu, Xiaodan; Si, Wen; Si, Jianguo 1 2020 On the number of limit cycles in generalized Abel equations. Zbl 1472.34065Huang, Jianfeng; Torregrosa, Joan; Villadelprat, Jordi 1 2020 Extended and symmetric loss of stability for canards in planar fast-slow maps. Zbl 1478.37054Engel, Maximilian; Jardón-Kojakhmetov, Hildeberto 1 2020 Data-driven identification of parametric partial differential equations. Zbl 1456.65096Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan 23 2019 Linearly recurrent autoencoder networks for learning dynamics. Zbl 07068540Otto, Samuel E.; Rowley, Clarence W. 22 2019 A collisionless singular Cucker-Smale model with decentralized formation control. Zbl 1432.34063Choi, Young-Pil; Kalise, Dante; Peszek, Jan; Peters, Andrés A. 16 2019 Bifurcation analysis of a Mosquito population model with a saturated release rate of sterile mosquitoes. Zbl 1428.34066Huang, Jicai; Ruan, Shigui; Yu, Pei; Zhang, Yuyue 12 2019 A second-order particle swarm model on a sphere and emergent dynamics. Zbl 1412.34157Ha, Seung-Yeal; Kim, Dohyun 11 2019 Online dynamic mode decomposition for time-varying systems. Zbl 07122844Zhang, Hao; Rowley, Clarence W.; Deem, Eric A.; Cattafesta, Louis N. 11 2019 The linear stability of symmetric spike patterns for a bulk-membrane coupled Gierer-Meinhardt model. Zbl 1419.35107Gomez, Daniel; Ward, Michael J.; Wei, Juncheng 9 2019 Randomized dynamic mode decomposition. Zbl 1427.65410Erichson, N. Benjamin; Mathelin, Lionel; Kutz, J. Nathan; Brunton, Steven L. 8 2019 Spectral filtering of interpolant observables for a discrete-in-time downscaling data assimilation algorithm. Zbl 1428.35276Celik, Emine; Olson, Eric; Titi, Edriss S. 8 2019 Stability of traveling waves for reaction-diffusion equations with multiplicative noise. Zbl 1414.35117Hamster, C. H. S.; Hupkes, H. J. 8 2019 Discovery of nonlinear multiscale systems: sampling strategies and embeddings. Zbl 1474.65476Champion, Kathleen P.; Brunton, Steven L.; Kutz, J. Nathan 8 2019 Pattern formation and synchronism in an allelopathic plankton model with delay in a network. Zbl 1416.34071Tian, Canrong; Ruan, Shigui 7 2019 Drift of spectrally stable shifted states on star graphs. Zbl 1435.35401Kairzhan, Adilbek; Pelinovsky, Dmitry E.; Goodman, Roy H. 7 2019 Nonlinear dynamics in queueing theory: determining the size of oscillations in queues with delay. Zbl 1417.34202Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 7 2019 The Kuramoto model on oriented and signed graphs. Zbl 1420.34083Delabays, Robin; Jacquod, Philippe; Dörfler, Florian 7 2019 Persistent homology of Morse decompositions in combinatorial dynamics. Zbl 1415.37058Dey, Tamal K.; Juda, Mateusz; Kapela, Tomasz; Kubica, Jacek; Lipiński, Michał; Mrozek, Marian 6 2019 Number and stability of relaxation oscillations for predator-prey systems with small death rates. Zbl 1411.34064Hsu, Ting-Hao 6 2019 Pattern formation and oscillatory dynamics in a two-dimensional coupled bulk-surface reaction-diffusion system. Zbl 1428.37071Paquin-Lefebvre, Frédéric; Nagata, Wayne; Ward, Michael J. 6 2019 ...and 857 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 7,913 Authors 82 Ha, Seung-Yeal 46 Llibre, Jaume 42 Ward, Michael J. 41 Lessard, Jean-Philippe 39 Krauskopf, Bernd 36 Osinga, Hinke Maria 35 Mireles-James, Jason D. 33 Kühn, Christian 33 Kutz, J. Nathan 32 Bressloff, Paul C. 32 Wechselberger, Martin 30 Kevrekidis, Ioannis George 30 Sandstede, Björn 29 Brunton, Steven L. 29 Stewart, Ian Nicholas 27 Rubin, Jonathan E. 27 Scheel, Arnd 25 de la Llave, Rafael 24 Carrillo de la Plata, José Antonio 23 Coombes, Stephen 23 Desroches, Mathieu 23 Shen, Wenxian 23 Zhao, Xiao-Qiang 22 Kevrekidis, Panayotis G. 22 Mezić, Igor 22 Pelinovsky, Dmitry Efimovich 22 Wei, Juncheng 21 Laing, Carlo R. 21 Mischaikow, Konstantin 21 Park, Hansol 21 Teixeira, Marco Antonio 20 Hupkes, Hermen Jan 20 Kim, Dohyun 20 Novaes, Douglas Duarte 20 Ponce, Enrique 20 Uldall Kristiansen, K. 20 van den Berg, Jan Bouwe 20 van Heijster, Peter 19 Adimy, Mostafa 19 Ashwin, Peter 19 Knobloch, Edgar 19 Kolokolnikov, Theodore 19 Moehlis, Jeff 19 Wang, Bixiang 19 Zgliczyński, Piotr 18 Balasuriya, Sanjeeva 18 Chen, Guanrong 18 Craciun, Gheorghe 18 Doelman, Arjen 18 Golubitsky, Martin A. 18 Jeffrey, Mike R. 18 Krupa, Martin 18 Porfiri, Maurizio 17 de Carvalho, Tiago 17 Dias, Ana Paula S. 17 Kilpatrick, Zachary P. 17 Lawley, Sean D. 17 Sherratt, Jonathan A. 17 Wilson, Dan D. 16 Blömker, Dirk 16 Bollt, Erik M. 16 Faye, Grégory 16 Fetecau, Razvan C. 15 Aguiar, Manuela A. D. 15 Cao, Jinde 15 Park, Jinyeong 15 Rademacher, Jens Diederich Michael 15 Wyller, John A. 14 Belykh, Igor V. 14 Duan, Jinqiao 14 Gardini, Laura 14 Li, Zhuchun 14 Mrozek, Marian 14 Shi, Junping 14 Simpson, David John Warwick 14 Wanner, Thomas 14 Xu, Jian 13 Crauste, Fabien 13 Feliu, Elisenda 13 Kaper, Tasso J. 13 Palacián, Jesús F. 13 M-Seara, Tere 13 Tonon, Durval José 13 Yang, Xiaosong 13 Yanguas, Patricia 13 Zhang, Mingji 12 Bramburger, Jason J. 12 Cai, Yongli 12 Froyland, Gary 12 Ghosh, Dibakar 12 Giannakis, Dimitrios 12 Lăzureanu, Cristian 12 Liu, Weishi 12 Tang, Sanyi 12 Wang, Weiming 12 Yu, Wenwu 11 Alla, Alessandro 11 Anderson, David Frederick 11 Avitabile, Daniele 11 Barrio, Roberto ...and 7,813 more Authors all top 5 Cited in 460 Journals 391 SIAM Journal on Applied Dynamical Systems 328 Physica D 306 Chaos 275 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 253 Journal of Differential Equations 154 Journal of Nonlinear Science 150 Discrete and Continuous Dynamical Systems. Series B 128 Communications in Nonlinear Science and Numerical Simulation 117 Nonlinear Dynamics 116 Journal of Mathematical Analysis and Applications 107 Journal of Mathematical Biology 104 Nonlinearity 101 Journal of Dynamics and Differential Equations 97 Bulletin of Mathematical Biology 90 Journal of Fluid Mechanics 89 Applied Mathematics and Computation 82 Nonlinear Analysis. Real World Applications 78 SIAM Journal on Applied Mathematics 77 Discrete and Continuous Dynamical Systems 75 Chaos, Solitons and Fractals 73 Journal of Computational Physics 70 Automatica 68 Journal of Theoretical Biology 56 The Journal of Mathematical Neuroscience 55 SIAM Journal on Mathematical Analysis 52 Journal of Computational and Applied Mathematics 50 Journal of Statistical Physics 48 Journal of Mathematical Physics 48 Mathematical Biosciences 48 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 45 Qualitative Theory of Dynamical Systems 45 Mathematical Biosciences and Engineering 44 Journal of Computational Neuroscience 43 Applied Mathematics Letters 41 Regular and Chaotic Dynamics 40 Biological Cybernetics 36 Celestial Mechanics and Dynamical Astronomy 33 SIAM Journal on Scientific Computing 32 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 31 European Journal of Applied Mathematics 31 Journal of Computational Dynamics 30 Neural Computation 30 Dynamical Systems 29 Archive for Rational Mechanics and Analysis 29 Journal of the Franklin Institute 29 Mathematical Modelling of Natural Phenomena 29 Discrete and Continuous Dynamical Systems. Series S 28 Computer Methods in Applied Mechanics and Engineering 27 Abstract and Applied Analysis 26 Computers & Mathematics with Applications 26 Applied Mathematical Modelling 26 Communications on Pure and Applied Analysis 25 Applicable Analysis 25 ZAMP. Zeitschrift für angewandte Mathematik und Physik 25 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 24 Communications in Mathematical Physics 24 Acta Applicandae Mathematicae 23 Journal of Difference Equations and Applications 23 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 22 Mathematical Problems in Engineering 21 SIAM Journal on Control and Optimization 21 SIAM Review 21 Advances in Difference Equations 20 Proceedings of the American Mathematical Society 20 Journal of Biological Dynamics 19 Mathematics and Computers in Simulation 19 Quarterly of Applied Mathematics 19 Nonlinear Analysis. Hybrid Systems 18 Systems & Control Letters 17 Physica A 17 Physics Letters. A 17 Studies in Applied Mathematics 17 Networks and Heterogeneous Media 16 Transactions of the American Mathematical Society 16 Journal of Scientific Computing 16 Complexity 16 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 16 Multiscale Modeling & Simulation 15 Mathematical Methods in the Applied Sciences 15 Numerische Mathematik 14 Japan Journal of Industrial and Applied Mathematics 14 Advances in Computational Mathematics 14 Journal of Mathematical Chemistry 14 Discrete Dynamics in Nature and Society 14 International Journal of Biomathematics 13 Journal of Functional Analysis 13 SIAM Journal on Numerical Analysis 13 Neural Networks 13 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 13 Kinetic and Related Models 13 SIAM/ASA Journal on Uncertainty Quantification 12 Ergodic Theory and Dynamical Systems 12 Applied Numerical Mathematics 12 Journal of Mathematical Sciences (New York) 12 Foundations of Computational Mathematics 11 Advances in Mathematical Physics 11 Journal of Applied Analysis and Computation 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Indagationes Mathematicae. New Series ...and 360 more Journals all top 5 Cited in 61 Fields 1,961 Ordinary differential equations (34-XX) 1,946 Dynamical systems and ergodic theory (37-XX) 1,938 Biology and other natural sciences (92-XX) 1,828 Partial differential equations (35-XX) 734 Numerical analysis (65-XX) 553 Systems theory; control (93-XX) 481 Mechanics of particles and systems (70-XX) 423 Fluid mechanics (76-XX) 367 Probability theory and stochastic processes (60-XX) 245 Statistical mechanics, structure of matter (82-XX) 173 Mechanics of deformable solids (74-XX) 165 Computer science (68-XX) 163 Calculus of variations and optimal control; optimization (49-XX) 147 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 126 Operations research, mathematical programming (90-XX) 124 Operator theory (47-XX) 110 Integral equations (45-XX) 107 Statistics (62-XX) 96 Combinatorics (05-XX) 95 Information and communication theory, circuits (94-XX) 92 Difference and functional equations (39-XX) 78 Optics, electromagnetic theory (78-XX) 71 Quantum theory (81-XX) 70 Classical thermodynamics, heat transfer (80-XX) 58 Global analysis, analysis on manifolds (58-XX) 55 Differential geometry (53-XX) 48 Geophysics (86-XX) 44 Linear and multilinear algebra; matrix theory (15-XX) 37 Real functions (26-XX) 20 Algebraic topology (55-XX) 19 Approximations and expansions (41-XX) 17 Functional analysis (46-XX) 16 Commutative algebra (13-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 16 Convex and discrete geometry (52-XX) 16 Relativity and gravitational theory (83-XX) 15 Astronomy and astrophysics (85-XX) 14 Special functions (33-XX) 13 Manifolds and cell complexes (57-XX) 12 General and overarching topics; collections (00-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 General topology (54-XX) 10 Algebraic geometry (14-XX) 10 Measure and integration (28-XX) 9 Group theory and generalizations (20-XX) 7 Topological groups, Lie groups (22-XX) 6 Number theory (11-XX) 6 Field theory and polynomials (12-XX) 5 History and biography (01-XX) 4 Potential theory (31-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Mathematical logic and foundations (03-XX) 3 Functions of a complex variable (30-XX) 3 Geometry (51-XX) 3 Mathematics education (97-XX) 2 Category theory; homological algebra (18-XX) 2 Integral transforms, operational calculus (44-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