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: 1,283 Publications (since 2002) References Indexed: 732 Publications with 31,227 References. all top 5 Latest Issues 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 16 Kutz, J. Nathan 16 Uldall Kristiansen, K. 15 Rubin, Jonathan E. 14 Champneys, Alan R. 14 Ward, Michael J. 13 Bressloff, Paul C. 13 Golubitsky, Martin A. 13 Guckenheimer, John M. 13 Ha, Seung-Yeal 12 Meiss, James D. 11 Mischaikow, Konstantin 11 Rademacher, Jens Diederich Michael 11 Wechselberger, Martin 10 de la Llave, Rafael 10 Mireles-James, Jason D. 10 Sandstede, Björn 9 Bollt, Erik M. 9 Doelman, Arjen 9 Hogan, S. John 9 Lessard, Jean-Philippe 9 Porter, Mason Alexander 9 Wilson, Dan D. 8 Brunton, Steven L. 8 Ermentrout, Bard G. 8 Ermentrout, George Bard 8 Kilpatrick, Zachary P. 8 Kirk, Vivien 8 Kolokolnikov, Theodore 8 Mezić, Igor 8 Moehlis, Jeff 8 Pelinovsky, Dmitry Efimovich 8 Scheel, Arnd 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 Knobloch, Edgar 7 Kühn, Christian 7 Postlethwaite, Claire M. 7 Rucklidge, Alastair M. 7 Sieber, Jan 7 Stewart, Ian Nicholas 7 Zgliczyński, Piotr 6 Ashwin, Peter 6 Coombes, Stephen 6 Dullin, Holger R. 6 Kopell, Nancy J. 6 Lloyd, David J. B. 6 Palacián, Jesús F. 6 Starke, Jens 6 Terman, David Hillel 6 van den Berg, Jan Bouwe 6 Wilczak, Daniel 6 Yanchuk, Sergiĭ Volodymyrovych 6 Yanguas, Patricia 5 Avitabile, Daniele 5 Balasuriya, Sanjeeva 5 Colombo, Alessandro G. 5 Cummins, Bree 5 Fetecau, Razvan C. 5 Folias, Stefanos E. 5 Froyland, Gary 5 Giesl, Peter 5 Gottwald, Georg A. 5 Hüls, Thorsten 5 Hupkes, Hermen Jan 5 Kuznetsov, Yuri Alexandrovich 5 Lee, Euiwoo 5 Lewis, Mark Alun 5 Lewis, Timothy J. 5 Mrozek, Marian 5 Rom-Kedar, Vered 5 Rotstein, Horacio G. 5 Rowley, Clarence Worth 5 Teixeira, Marco Antonio 5 Vidal, Claudio 5 Wanner, Thomas 5 Wayne, Clarence Eugene 5 Wulff, Claudia 4 Aguirre, Pablo 4 Atay, Fatihcan M. 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 Chow, Carson C. 4 Cors, Josep Maria 4 Dankowicz, Harry J. 4 Dawes, Jonathan H. P. 4 Day, Sarah L. ...and 1,957 more Authors all top 5 Fields 725 Dynamical systems and ergodic theory (37-XX) 534 Ordinary differential equations (34-XX) 385 Biology and other natural sciences (92-XX) 304 Partial differential equations (35-XX) 182 Numerical analysis (65-XX) 165 Mechanics of particles and systems (70-XX) 83 Systems theory; control (93-XX) 79 Probability theory and stochastic processes (60-XX) 75 Fluid mechanics (76-XX) 44 Statistical mechanics, structure of matter (82-XX) 37 Computer science (68-XX) 33 Combinatorics (05-XX) 32 Mechanics of deformable solids (74-XX) 32 Optics, electromagnetic theory (78-XX) 30 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 29 Operations research, mathematical programming (90-XX) 27 Calculus of variations and optimal control; optimization (49-XX) 26 Difference and functional equations (39-XX) 24 Statistics (62-XX) 23 Integral equations (45-XX) 21 Operator theory (47-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 18 Classical thermodynamics, heat transfer (80-XX) 14 Geophysics (86-XX) 14 Information and communication theory, circuits (94-XX) 8 Approximations and expansions (41-XX) 8 General topology (54-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Quantum theory (81-XX) 7 Convex and discrete geometry (52-XX) 7 Differential geometry (53-XX) 7 Algebraic topology (55-XX) 6 Group theory and generalizations (20-XX) 6 Manifolds and cell complexes (57-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Algebraic geometry (14-XX) 4 Measure and integration (28-XX) 4 Functional analysis (46-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-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 1,048 Publications have been cited 12,078 times in 7,632 Documents Cited by ▼ Year ▼ Basic reproduction numbers for reaction-diffusion epidemic models. Zbl 1259.35120Wang, Wendi; Zhao, Xiao-Qiang 264 2012 Wave structure and nonlinear balances in a family of evolutionary PDEs. Zbl 1088.76531Holm, Darryl D.; Staley, Martin F. 144 2003 Symmetry groupoids and patterns of synchrony in coupled cell networks. Zbl 1089.34032Stewart, Ian; Golubitsky, Martin; Pivato, Marcus 126 2003 On the critical coupling for Kuramoto oscillators. Zbl 1242.34096Dörfler, Florian; Bullo, Francesco 125 2011 Canonical discontinuous planar piecewise linear systems. Zbl 1242.34020Freire, Emilio; Ponce, Enrique; Torres, Francisco 124 2012 Patterns of synchrony in coupled cell networks with multiple arrows. Zbl 1090.34030Golubitsky, Martin; Stewart, Ian; Török, Andrei 118 2005 Global synchronization of linearly hybrid coupled networks with time-varying delay. Zbl 1161.94011Yu, Wenwu; Cao, Jinde; Lü, Jinhu 107 2008 Existence and bifurcation of canards in \(\mathbb R^3\) in the case of a folded node. Zbl 1090.34047Wechselberger, Martin 103 2005 Sufficient conditions for fast switching synchronization in time-varying network topologies. Zbl 1145.37345Stilwell, Daniel J.; Bollt, Erik M.; Roberson, D. Gray 87 2006 Dynamic mode decomposition with control. Zbl 1334.65199Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan 85 2016 Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator. Zbl 1381.37096Arbabi, Hassan; Mezić, Igor 76 2017 Spatiotemporal dynamics of the diffusive mussel-algae model near Turing-Hopf bifurcation. Zbl 1382.35035Song, Yongli; Jiang, Heping; Liu, Quan-Xing; Yuan, Yuan 68 2017 Nonlinear patterns in urban crime: hotspots, bifurcations, and suppression. Zbl 1282.91273Short, M. B.; Bertozzi, A. L.; Brantingham, P. J. 63 2010 A primer of swarm equilibria. Zbl 1255.35012Bernoff, Andrew J.; Topaz, Chad M. 63 2011 Neuronal networks with gap junctions: a study of piecewise linear planar neuron models. Zbl 1159.92008Coombes, S. 63 2008 PDE methods for nonlocal models. Zbl 1088.34011Laing, Carlo R.; Troy, William C. 63 2003 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. 62 2004 Mixed-mode oscillations in three time-scale systems: a prototypical example. Zbl 1167.34346Krupa, Martin; Popović, Nikola; Kopell, Nancy 59 2008 On the implementation of the 0-1 test for chaos. Zbl 1161.37054Gottwald, Georg A.; Melbourne, Ian 58 2009 Global phase-locking in finite populations of phase-coupled oscillators. Zbl 1167.34330Verwoerd, Mark; Mason, Oliver 55 2008 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025Guckenheimer, John 54 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. 53 2005 Evans functions for integral neural field equations with Heaviside firing rate function. Zbl 1067.92019Coombes, S.; Owen, M. R. 53 2004 Classification of asymptotic behavior in a stochastic SIR model. Zbl 1343.34109Dieu, N. T.; Nguyen, D. H.; Du, N. H.; Yin, G. 53 2016 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 52 2009 Localized hexagon patterns of the planar Swift-Hohenberg equation. Zbl 1168.35311Lloyd, David J. B.; Sandstede, Björn; Avitabile, Daniele; Champneys, Alan R. 52 2008 Long period oscillations in a \(G_{0}\) model of hematopoietic stem cells. Zbl 1110.34050Pujo-Menjouet, Laurent; Bernard, Samuel; Mackey, Michael C. 52 2005 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. 52 2007 Defects in oscillatory media: toward a classification. Zbl 1059.37062Sandstede, Björn; Scheel, Arnd 51 2004 Interacting Langevin diffusions: gradient structure and ensemble Kalman sampler. Zbl 1447.65119Garbuno-Inigo, Alfredo; Hoffmann, Franca; Li, Wuchen; Stuart, Andrew M. 50 2020 Random attractors for delay parabolic equations with additive noise and deterministic nonautonomous forcing. Zbl 1317.60081Wang, Xiaohu; Lu, Kening; Wang, Bixiang 49 2015 A geometric approach to the global attractor conjecture. Zbl 1301.34063Gopalkrishnan, Manoj; Miller, Ezra; Shiu, Anne 49 2014 A computational and geometric approach to phase resetting curves and surfaces. Zbl 1216.34030Guillamon, Antoni; Huguet, Gemma 48 2009 Multiresolution dynamic mode decomposition. Zbl 1338.37121Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. 48 2016 \(R_0\) analysis of a spatiotemporal model for a stream population. Zbl 1252.35068Mckenzie, H. W.; Jin, Y.; Jacobsen, J.; Lewis, M. A. 47 2012 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 47 2003 Breathing pulses in an excitatory neural network. Zbl 1058.92010Folias, Stefanos E.; Bressloff, Paul C. 47 2004 HJB-POD-based feedback design for the optimal control of evolution problems. Zbl 1058.35061Kunisch, K.; Volkwein, S.; Xie, L. 47 2004 Power-law kinetics and determinant criteria for the preclusion of multistationarity in networks of interacting species. Zbl 1278.92012Wiuf, Carsten; Feliu, Elisenda 47 2013 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. 46 2016 Freezing solutions of equivariant evolution equations. Zbl 1061.65078Beyn, W.-J.; Thümmler, V. 44 2004 The stability and dynamics of localized spot patterns in the two-dimensional Gray-Scott model. Zbl 1223.35033Chen, W.; Ward, M. J. 43 2011 Kink-antikink collisions in the \(\phi^4\) equation: the \(n\)-bounce resonance and the separatrix map. Zbl 1145.74370Goodman, Roy H.; Haberman, Richard 43 2005 Higher order dynamic mode decomposition. Zbl 1373.37169Le Clainche, Soledad; Vega, José M. 43 2017 Nondeterministic chaos, and the two-fold singularity in piecewise smooth flows. Zbl 1227.34044Colombo, Alessandro; Jeffrey, Mike R. 42 2011 Complete entrainment of Lohe oscillators under attractive and repulsive couplings. Zbl 1310.34060Choi, Sun-Ho; Ha, Seung-Yeal 42 2014 On computing the critical coupling coefficient for the Kuramoto model on a complete bipartite graph. Zbl 1167.34331Verwoerd, Mark; Mason, Oliver 41 2009 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 41 2016 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005Guckenheimer, John; Oliva, Ricardo A. 40 2002 Asymptotic dynamics of attractive-repulsive swarms. Zbl 1168.92045Leverentz, Andrew J.; Topaz, Chad M.; Bernoff, Andrew J. 40 2009 The two-fold singularity of discontinuous vector fields. Zbl 1178.34042Jeffrey, M. R.; Colombo, A. 40 2009 Data-driven identification of parametric partial differential equations. Zbl 1456.65096Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan 40 2019 Nonsmooth Lagrangian mechanics and variational collision integrators. Zbl 1088.37045Fetecau, R. C.; Marsden, J. E.; Ortiz, M.; West, M. 39 2003 Uniform attractors for nonautonomous wave equations with nonlinear damping. Zbl 1210.35160Sun, Chunyou; Cao, Daomin; Duan, Jinqiao 38 2007 Dynamics at a switching intersection: hierarchy, isonomy, and multiple sliding. Zbl 1310.34018Jeffrey, Mike R. 38 2014 Noise-induced behaviors in neural mean field dynamics. Zbl 1235.92016Touboul, Jonathan; Hermann, Geoffroy; Faugeras, Olivier 37 2012 To snake or not to snake in the planar Swift-Hohenberg equation. Zbl 1200.37014Avitabile, Daniele; Lloyd, David J. B.; Burke, John; Knobloch, Edgar; Sandstede, Björn 36 2010 Study of singularities in nonsmooth dynamical systems via singular perturbation. Zbl 1167.34304Llibre, Jaume; Da Silva, Paulo R.; Teixeira, Marco A. 36 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. 36 2015 Computation of mixed type functional differential boundary value problems. Zbl 1090.65093Abell, Kate A.; Elmer, Christopher E.; Humphries, A. R.; Van Vleck, Erik S. 35 2005 Linearly recurrent autoencoder networks for learning dynamics. Zbl 1489.65164Otto, Samuel E.; Rowley, Clarence W. 35 2019 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060Guckenheimer, John; Kuehn, Christian 34 2010 Speeds of spread and propagation for KPP models in time almost and space periodic media. Zbl 1172.35423Huang, Jianhua; Shen, Wenxian 34 2009 Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system. Zbl 1167.34361Abaid, Nicole; Eisenberg, Robert S.; Liu, Weishi 34 2008 Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. Zbl 1058.35050Day, Sarah; Hiraoka, Yasuaki; Mischaikow, Konstantin; Ogawa, Toshiyuki 34 2005 Bifurcations in delay differential equations and applications to tumor and immune system interaction models. Zbl 1284.34118Bi, Ping; Ruan, Shigui 34 2013 Parameterization of invariant manifolds for periodic orbits. I: Efficient numerics via the Floquet normal form. Zbl 1376.37057Castelli, Roberto; Lessard, Jean-Philippe; Mireles James, J. D. 34 2015 Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion. Zbl 1302.35386Burger, Martin; Fetecau, Razvan; Huang, Yanghong 34 2014 Integration of dissipative partial differential equations: a case study. Zbl 1298.37071Arioli, Gianni; Koch, Hans 33 2010 Front propagation in stochastic neural fields. Zbl 1246.92004Bressloff, Paul C.; Webber, Matthew A. 33 2012 Existence and stability of standing pulses in neural networks. I: Existence. Zbl 1109.34002Guo, Yixin; Chow, Carson C. 33 2005 Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse. Zbl 1059.37067England, J. P.; Krauskopf, B.; Osinga, H. M. 33 2004 Wandering bumps in stochastic neural fields. Zbl 1278.92007Kilpatrick, Zachary P.; Ermentrout, Bard 33 2013 Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. Zbl 1330.37029Mireles James, J. D.; Mischaikow, Konstantin 33 2013 An analytical approach to codimension-2 sliding bifurcations in the dry-friction oscillator. Zbl 1201.37086Guardia, Marcel; Hogan, S. John; Seara, Tere M. 32 2010 Computing slow manifolds of saddle type. Zbl 1176.37026Guckenheimer, John; Kuehn, Christian 32 2009 The Melnikov method and subharmonic orbits in a piecewise-smooth system. Zbl 1262.37028Granados, A.; Hogan, S. J.; Seara, T. M. 32 2012 TC-HAT (\(\widehat{TC}\)): a novel toolbox for the continuation of periodic trajectories in hybrid dynamical systems. Zbl 1192.34004Thota, Phanikrishna; Dankowicz, Harry 32 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 32 2008 Random attractor for damped nonlinear wave equations with white noise. Zbl 1094.35154Zhou, Shengfan; Yin, Fuqi; Ouyang, Zigen 32 2005 Continuation of quasi-periodic invariant tori. Zbl 1090.37057Schilder, Frank; Osinga, Hinke M.; Vogt, Werner 32 2005 Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108Huguet, Gemma; de la Llave, Rafael 32 2013 Local/global analysis of the stationary solutions of some neural field equations. Zbl 1194.92015Veltz, Romain; Faugeras, Olivier 31 2010 Homoclinic stripe patterns. Zbl 1004.35063Doelman, Arjen; van der Ploeg, Harmen 31 2002 The slow dynamics of two-spike solutions for the Gray-Scott and Gierer-Meinhardt systems: competition and oscillatory instabilities. Zbl 1145.35404Sun, Wentao; Ward, Michael J.; Russell, Robert 31 2005 Semistrong pulse interactions in a class of coupled reaction-diffusion equations. Zbl 1088.35517Doelman, Arjen; Kaper, Tasso J. 31 2003 Neural fields with distributed transmission speeds and long-range feedback delays. Zbl 1210.34118Atay, Fatihcan M.; Hutt, Axel 31 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 31 2007 On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain. Zbl 1267.35027Cvitanović, Predrag; Davidchack, Ruslan L.; Siminos, Evangelos 30 2010 Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation. Zbl 1408.37062van den Berg, Jan Bouwe; Lessard, Jean-Philippe 30 2008 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 30 2006 \(R_0\) analysis of a benthic-drift model for a stream population. Zbl 1364.92059Huang, Qihua; Jin, Yu; Lewis, Mark A. 30 2016 On the use of blowup to study regularizations of singularities of piecewise smooth dynamical systems in \(\mathbb{R}^3\). Zbl 1370.37100Kristiansen, K. Uldall; Hogan, S. J. 30 2015 A collisionless singular Cucker-Smale model with decentralized formation control. Zbl 1432.34063Choi, Young-Pil; Kalise, Dante; Peszek, Jan; Peters, Andrés A. 29 2019 Some canonical bifurcations in the Swift-Hohenberg equation. Zbl 1210.34028Peletier, L. A.; Williams, J. F. 29 2007 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 29 2014 A computational method to extract macroscopic variables and their dynamics in multiscale systems. Zbl 1320.37012Froyland, Gary; Gottwald, Georg A.; Hammerlindl, Andy 29 2014 Dynamics on networks of cluster states for globally coupled phase oscillators. Zbl 1167.34326Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart 28 2007 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 28 2003 The structure of MESSI biological systems. Zbl 1395.92071Pérez Millán, Mercedes; Dickenstein, Alicia 28 2018 Continuation with noninvasive control schemes: revealing unstable states in a pedestrian evacuation scenario. Zbl 07674585Panagiotopoulos, Ilias; Starke, Jens; Sieber, Jan; Just, Wolfram 2 2023 Phase oscillator networks with nonlocal higher-order interactions: twisted states, stability, and bifurcations. Zbl 07723354Bick, Christian; Böhle, Tobias; Kuehn, Christian 2 2023 Non-Markovian models of opinion dynamics on temporal networks. Zbl 07741169Chu, Weiqi; Porter, Mason A. 2 2023 Hyperdissipative Navier-Stokes equations driven by time-dependent forces: invariant manifolds. Zbl 07674591Wang, Rong-Nian; Zhao, Jia-Cheng; Miranville, Alain 1 2023 Resonances and phase locking phenomena for foliation preserving torus maps. Zbl 1515.37060He, Xiaolong; de la Llave, Rafael 1 2023 Mixed-mode oscillations in coupled Fitzhugh-Nagumo oscillators: blow-up analysis of cusped singularities. Zbl 1521.34058Kristiansen, Kristian Uldall; Pedersen, Morten Gram 1 2023 A pulsed-precipitation model of dryland vegetation pattern formation. Zbl 1518.35071Gandhi, Punit; Liu, Lily; Silber, Mary 1 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 1520.34046Lu, Min; Huang, Jicai; Wang, Hao 1 2023 Degenerate Turing bifurcation and the birth of localized patterns in activator-inhibitor systems. Zbl 07723356Villar-Sepúlveda, Edgardo; Champneys, Alan 1 2023 Persistence of periodic orbits under state-dependent delayed perturbations: computer-assisted proofs. Zbl 07723358Gimeno, Joan; Lessard, Jean-Philippe; Mireles James, J. D.; Yang, Jiaqi 1 2023 Extinction of multiple populations and a team of die-out Lyapunov functions. Zbl 07741161Akhavan, Naghmeh; Yorke, James A. 1 2023 Stability analysis of the immune system induced by chemotaxis. Zbl 07741166Zheng, Pan; Shan, Wenhai; Liao, Guangyuan 1 2023 On a competition-diffusion-advection system from river ecology: mathematical analysis and numerical study. Zbl 1484.35034Yan, Xiao; Nie, Hua; Zhou, Peng 13 2022 Modeling multilane traffic with moving obstacles by nonlocal balance laws. Zbl 1497.35315Bayen, Alexandre; Friedrich, Jan; Keimer, Alexander; Pflug, Lukas; Veeravalli, Tanya 6 2022 A dynamical theory for singular stochastic delay differential equations. I: Linear equations and a multiplicative ergodic theorem on fields of Banach spaces. Zbl 1490.34103Varzaneh, M. Ghani; Riedel, S.; Scheutzow, M. 5 2022 Local and global existence for nonlocal multispecies advection-diffusion models. Zbl 1494.35002Giunta, Valeria; Hillen, Thomas; Lewis, Mark; Potts, Jonathan R. 4 2022 Derivative-free Bayesian inversion using multiscale dynamics. Zbl 1493.62132Pavliotis, G. A.; Stuart, A. M.; Vaes, U. 4 2022 Modulation and amplitude equations on bounded domains for nonlinear SPDEs driven by cylindrical \(\alpha\)-stable Lévy processes. Zbl 1492.60197Yuan, Shenglan; Bloemker, Dirk 3 2022 Dynamics of small particle inertial migration in curved square ducts. Zbl 1486.76098Ha, Kyung; Harding, Brendan; Bertozzi, Andrea L.; Stokes, Yvonne M. 3 2022 Graphop mean-field limits for Kuramoto-type models. Zbl 1483.35270Gkogkas, Marios Antonios; Kuehn, Christian 3 2022 Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock. Zbl 1509.34045Castro, Sofia B. S. D.; Ferreira, Ana; Garrido-da-Silva, Liliana; Labouriau, Isabel S. 3 2022 Efficient computation of linear response of chaotic attractors with one-dimensional unstable manifolds. Zbl 1497.37103Chandramoorthy, Nisha; Wang, Qiqi 2 2022 A bounded-confidence model of opinion dynamics on hypergraphs. Zbl 1482.91163Hickok, Abigail; Kureh, Yacoub; Brooks, Heather Z.; Feng, Michelle; Porter, Mason A. 2 2022 Emergent behaviors of rotation matrix flocks. Zbl 1513.70057Fetecau, Razvan C.; Ha, Seung-Yeal; Park, Hansol 2 2022 Bifurcations and dynamics in inertial focusing of particles in curved rectangular ducts. Zbl 1503.76041Valani, Rahil N.; Harding, Brendan; Stokes, Yvonne M. 2 2022 Ensemble inference methods for models with noisy and expensive likelihoods. Zbl 1493.62124Dunbar, Oliver R. A.; Duncan, Andrew B.; Stuart, Andrew M.; Wolfram, Marie-Therese 1 2022 Sequential attractors in combinatorial threshold-linear networks. 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Zbl 1486.35116Matano, Hiroshi; Mori, Yoichiro; Nara, Mitsunori; Sakakibara, Koya 1 2022 Anti-integrability for three-dimensional quadratic maps. Zbl 07506062Hampton, Amanda E.; Meiss, James D. 1 2022 Persistence of Conley-Morse graphs in combinatorial dynamical systems. Zbl 1498.37069Dey, Tamal K.; Mrozek, Marian; Slechta, Ryan 1 2022 Stochastically adaptive control and synchronization: from globally one-sided Lipschitzian to only locally Lipschitzian systems. Zbl 1492.60182Zhou, Shijie; Lai, Ying-Cheng; Lin, Wei 1 2022 Mechanistic modeling of longitudinal shape changes: equations of motion and inverse problems. Zbl 1481.49045Hsieh, Dai-Ni; Arguillère, Sylvain; Charon, Nicolas; Younes, Laurent 1 2022 Dynamical analysis and optimization of a generalized resource allocation model of microbial growth. 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Zbl 1441.82011Ha, Seung-Yeal; Park, Hansol 12 2020 ...and 948 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 9,589 Authors 99 Ha, Seung-Yeal 56 Llibre, Jaume 47 Krauskopf, Bernd 45 Ward, Michael J. 44 Lessard, Jean-Philippe 41 Kühn, Christian 40 Mireles-James, Jason D. 40 Osinga, Hinke Maria 36 Kutz, J. Nathan 35 Kevrekidis, Ioannis George 34 Bressloff, Paul C. 34 Brunton, Steven L. 34 Scheel, Arnd 32 Sandstede, Björn 32 Wechselberger, Martin 31 Rubin, Jonathan E. 31 Stewart, Ian Nicholas 29 Carrillo de la Plata, José Antonio 28 Kevrekidis, Panayotis G. 27 de la Llave, Rafael 27 Mezić, Igor 27 Park, Hansol 27 Zhao, Xiao-Qiang 26 Novaes, Douglas Duarte 26 Teixeira, Marco Antonio 26 Uldall Kristiansen, K. 26 Wei, Juncheng 25 Craciun, Gheorghe 25 Pelinovsky, Dmitry Efimovich 25 Shen, Wenxian 24 Hupkes, Hermen Jan 24 Mischaikow, Konstantin 23 Coombes, Stephen 23 Desroches, Mathieu 23 Kim, Dohyun 23 Kolokolnikov, Theodore 22 Ponce, Enrique 21 Doelman, Arjen 21 Laing, Carlo R. 21 van den Berg, Jan Bouwe 21 van Heijster, Peter 21 Wang, Bixiang 21 Wang, Jinliang 20 Adimy, Mostafa 20 Ashwin, Peter 20 Chen, Guanrong 20 de Carvalho, Tiago 20 Jeffrey, Mike R. 20 Moehlis, Jeff 20 Wilson, Dan D. 19 Balasuriya, Sanjeeva 19 Dias, Ana Paula S. 19 Duan, Jinqiao 19 Golubitsky, Martin A. 19 Knobloch, Edgar 19 Porfiri, Maurizio 19 Simpson, David John Warwick 19 Zgliczyński, Piotr 18 Bollt, Erik M. 18 Cao, Jinde 18 Faye, Grégory 18 Fetecau, Razvan C. 18 Kilpatrick, Zachary P. 18 Krupa, Martin 18 Rademacher, Jens Diederich Michael 18 Sherratt, Jonathan A. 17 Aguiar, Manuela A. D. 17 Blömker, Dirk 17 Feliu, Elisenda 17 Ghosh, Dibakar 17 Lawley, Sean D. 17 Zhang, Mingji 16 Bi, Qinsheng 16 Cai, Yongli 16 Wang, Weiming 16 Wanner, Thomas 15 Froyland, Gary 15 Gao, Hongjun 15 Gardini, Laura 15 Gedeon, Tomáš 15 Kaper, Tasso J. 15 Li, Shimin 15 Li, Zhuchun 15 Meiss, James D. 15 Mrozek, Marian 15 Park, Jinyeong 15 Shi, Junping 15 Sieber, Jan 15 Teng, Zhi-dong 15 Wang, Hao 15 Wyller, John A. 14 Alla, Alessandro 14 Barrio, Roberto 14 Belykh, Igor V. 14 Bick, Christian 14 Giannakis, Dimitrios 14 Huang, Lihong 14 M-Seara, Tere 14 Tonon, Durval José 14 Wu, Jianhong ...and 9,489 more Authors all top 5 Cited in 512 Journals 467 SIAM Journal on Applied Dynamical Systems 404 Physica D 308 Journal of Differential Equations 306 Chaos 292 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 201 Discrete and Continuous Dynamical Systems. 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A 20 Stochastics and Dynamics 20 Multiscale Modeling & Simulation 20 Networks and Heterogeneous Media 19 Journal of Scientific Computing 19 Kinetic and Related Models 18 Studies in Applied Mathematics 18 SIAM/ASA Journal on Uncertainty Quantification 17 Mathematical Methods in the Applied Sciences 17 Numerische Mathematik 17 Neural Networks 17 Japan Journal of Industrial and Applied Mathematics 17 Journal of Mathematical Chemistry 16 Transactions of the American Mathematical Society 16 Applied Numerical Mathematics 16 Advances in Computational 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 14 Inverse Problems 14 Discrete Dynamics in Nature and Society 14 Journal of Statistical Mechanics: Theory and Experiment 13 Journal of Functional Analysis 13 Ergodic Theory and Dynamical Systems 13 Journal of Mathematical Sciences (New York) 13 Foundations of Computational Mathematics ...and 412 more Journals all top 5 Cited in 61 Fields 2,385 Biology and other natural sciences (92-XX) 2,336 Ordinary differential equations (34-XX) 2,318 Dynamical systems and ergodic theory (37-XX) 2,283 Partial differential equations (35-XX) 917 Numerical analysis (65-XX) 701 Systems theory; control (93-XX) 579 Mechanics of particles and systems (70-XX) 532 Fluid mechanics (76-XX) 490 Probability theory and stochastic processes (60-XX) 301 Statistical mechanics, structure of matter (82-XX) 234 Computer science (68-XX) 199 Calculus of variations and optimal control; optimization (49-XX) 195 Mechanics of deformable solids (74-XX) 193 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 158 Operations research, mathematical programming (90-XX) 151 Operator theory (47-XX) 148 Statistics (62-XX) 127 Combinatorics (05-XX) 124 Integral equations (45-XX) 115 Difference and functional equations (39-XX) 106 Information and communication theory, circuits (94-XX) 94 Optics, electromagnetic theory (78-XX) 92 Quantum theory (81-XX) 84 Classical thermodynamics, heat transfer (80-XX) 67 Global analysis, analysis on manifolds (58-XX) 65 Geophysics (86-XX) 60 Differential geometry (53-XX) 52 Real functions (26-XX) 47 Linear and multilinear algebra; matrix theory (15-XX) 25 Algebraic geometry (14-XX) 25 Approximations and expansions (41-XX) 25 Algebraic topology (55-XX) 23 General and overarching topics; collections (00-XX) 23 Commutative algebra (13-XX) 19 Functional analysis (46-XX) 19 Convex and discrete geometry (52-XX) 17 Measure and integration (28-XX) 17 Special functions (33-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 17 Relativity and gravitational theory (83-XX) 16 Astronomy and astrophysics (85-XX) 14 General topology (54-XX) 14 Manifolds and cell complexes (57-XX) 13 Order, lattices, ordered algebraic structures (06-XX) 11 Group theory and generalizations (20-XX) 10 Field theory and polynomials (12-XX) 7 Topological groups, Lie groups (22-XX) 6 Number theory (11-XX) 5 History and biography (01-XX) 5 Functions of a complex variable (30-XX) 5 Potential theory (31-XX) 4 Mathematical logic and foundations (03-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geometry (51-XX) 2 Category theory; homological algebra (18-XX) 2 Mathematics education (97-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) Citations by Year