Edit Profile (opens in new tab) Guckenheimer, John M. Co-Author Distance Author ID: guckenheimer.john-m Published as: Guckenheimer, John; Guckenheimer, J.; Guckenheimer, John M. more...less Homepage: https://math.cornell.edu/john-m-guckenheimer External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 130 Publications since 1970, including 3 Books and 2 Additional arXiv Preprints 1 Contribution as Editor · 2 Further Contributions Biographic References: 1 Publication Co-Authors: 88 Co-Authors with 75 Joint Publications 2,990 Co-Co-Authors all top 5 Co-Authors 57 single-authored 5 Hoffman, Kathleen A. 5 Holmes, Philip J. 5 Weckesser, Warren 4 Kühn, Christian 4 Osinga, Hinke Maria 4 Oster, George F. 4 Willms, Allan R. 3 Harris-Warrick, Ronald M. 3 Kim, Seunghwan 3 Krauskopf, Bernd 3 MacKay, Robert Sinclair 2 Armbruster, Dieter 2 Choe, Won Gyu 2 Johnson, Stewart D. 2 Kopell, Nancy J. 2 Mahalov, Alex 2 Meerkamp, Philipp 2 Myers, Mark H. 2 Oliva, Ricardo A. 2 Rand, Richard H. 2 Scheper, Chris 2 Schlomiuk, Dana I. 2 Sherwood, William Erik 2 Timmermann, Axel 2 Vladimirsky, Alexander 2 Wechselberger, Martin 2 Worfolk, Patrick A. 2 Young, Lai-Sang 1 Arbib, Michael A. 1 Auslander, David M. 1 Baesens, Claude 1 Baro, Deborah J. 1 Bello-Rivas, Juan M. 1 Bergou, Attila J. 1 Berman, Gordon J. 1 Block, Louis Stuart 1 Bold, Katherine A. 1 Brillinger, David R. 1 Cao, Xiaodong 1 Carver, Sean G. 1 Chernoff, Paul R. 1 Childs, Gary 1 Chow, Shui-Nee 1 Cohen, Itai 1 Cowan, Jack D. 1 Cowan, Noah John 1 Dangelmayr, Gerhard 1 Dellnitz, Michael 1 Desroches, Mathieu 1 Dijkstra, Henk A. 1 Doedel, Eusebius J. 1 Edwards, Chantal 1 Ellner, Stephen P. 1 Ermentrout, George Bard 1 Full, Robert J. 1 Georgiou, Anastasia 1 Golomb, David 1 Golubitsky, Martin A. 1 Govaerts, Willy J. F. 1 Gueron, Shay 1 Guharay, Sabyasachi 1 Guttorp, Peter 1 Haiduc, Radu 1 Henderson, Michael E. 1 Howard, Louis N. 1 Hubbard, Judith 1 Iams, Sarah 1 Ilyashenko, Yulij Sergeevich 1 Ipaktchi, A. 1 Javeed, Aurya S. 1 Johnson, Tomas 1 Jones, Christopher K. R. T. 1 Junge, Oliver 1 Kauffman, Stuart Alan 1 Kevrekidis, Ioannis George 1 Khibnik, Alexander I. 1 Knobloch, Edgar 1 Koditschek, Dan 1 Labouriau, Isabel S. 1 Lamar, Michael Drew 1 Lanford, Oscar E. III 1 Levin, Simon Asher 1 Lizarraga, Ian 1 Mallet-Paret, John Joseph 1 Malo, Salvador 1 Marsden, Jerrold Eldon 1 McCracken, Marjorie F. 1 Meloon, Brian 1 Misiurewicz, Michał 1 Moser, Jürgen K. 1 Newhouse, Sheldon E. 1 Peck, Jack 1 Phipps, Eric T. 1 Rinzel, John 1 Ristroph, Leif 1 Ruiz, O. 1 Saloff-Coste, Laurent 1 Sandstede, Björn 1 Schecter, Stephen 1 Schmidt, Dieter S. ...and 10 more Co-Authors all top 5 Serials 13 SIAM Journal on Applied Dynamical Systems 7 Physica D 5 Nonlinearity 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Topology 3 Journal of Computational Neuroscience 3 Moscow Mathematical Journal 2 Archive for Rational Mechanics and Analysis 2 Biological Cybernetics 2 Communications in Mathematical Physics 2 Journal of Mathematical Biology 2 SIAM Journal on Numerical Analysis 2 SIAM Journal on Applied Mathematics 2 SIAM Review 2 SIAM Journal on Scientific Computing 2 Chaos 2 Applied Mathematical Sciences 1 Computer Methods in Applied Mechanics and Engineering 1 Geophysical and Astrophysical Fluid Dynamics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Bulletin of Mathematical Biology 1 The Mathematical Intelligencer 1 Annales de l’Institut Fourier 1 Compositio Mathematica 1 IEEE Transactions on Automatic Control 1 IEEE Transactions on Circuits and Systems 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Proceedings of the American Mathematical Society 1 Theoretical Population Biology 1 SIAM Journal on Mathematical Analysis 1 Expositiones Mathematicae 1 New Zealand Journal of Mathematics 1 Experimental Mathematics 1 Communications in Analysis and Geometry 1 Discrete and Continuous Dynamical Systems 1 Journal of Mathematical Chemistry 1 Annals of Mathematics. Second Series 1 Physical Review Letters 1 Bulletin of the American Mathematical Society 1 Contemporary Mathematics 1 MAA Studies in Mathematics 1 Progress in Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Anais da Academia Brasileira de Ciências 1 Journal of Computational Dynamics all top 5 Fields 84 Dynamical systems and ergodic theory (37-XX) 44 Ordinary differential equations (34-XX) 27 Biology and other natural sciences (92-XX) 22 Numerical analysis (65-XX) 16 Global analysis, analysis on manifolds (58-XX) 8 Partial differential equations (35-XX) 8 Fluid mechanics (76-XX) 7 Differential geometry (53-XX) 7 Mechanics of particles and systems (70-XX) 5 General topology (54-XX) 5 Systems theory; control (93-XX) 4 General and overarching topics; collections (00-XX) 3 Manifolds and cell complexes (57-XX) 3 Computer science (68-XX) 2 Measure and integration (28-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 111 Publications have been cited 6,528 times in 5,724 Documents Cited by ▼ Year ▼ Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001 Guckenheimer, John; Holmes, Philip 3,929 1983 The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale. Zbl 0346.58007 Marsden, J. E.; McCracken, M. 545 1976 Structural stability of Lorenz attractors. Zbl 0436.58018 Guckenheimer, John; Williams, R. F. 246 1979 Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012 Guckenheimer, John 183 1979 Mixed-mode oscillations with multiple time scales. Zbl 1250.34001 Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin 175 2012 The dynamics of density dependent population models. Zbl 0379.92016 Guckenheimer, J.; Oster, G.; Ipaktchi, A. 153 1977 Isochrons and phaseless sets. Zbl 0345.92001 Guckenheimer, J. 96 1975 Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027 Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 95 1988 A survey of methods for computing (un)stable manifolds of vector fields. Zbl 1086.34002 Krauskopf, B.; Osinga, H. M.; Doedel, E. J.; Henderson, M. E.; Guckenheimer, J.; Vladimirsky, A.; Dellnitz, M.; Junge, O. 92 2005 Structurally stable heteroclinic cycles. Zbl 0645.58022 Guckenheimer, John; Holmes, Philip 89 1988 Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036 Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S. 76 1991 Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028 Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang 70 1980 Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036 Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 60 1989 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025 Guckenheimer, John 55 2008 The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002 Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John 54 2006 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 48 2003 On the bifurcation of maps of the interval. Zbl 0354.58013 Guckenheimer, John 47 1977 Resonance regions for families of torus maps. Zbl 0678.58034 Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J. 41 1989 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005 Guckenheimer, John; Oliva, Ricardo A. 40 2002 On a four parameter family of planar vector fields. Zbl 0654.34025 Dangelmayr, G.; Guckenheimer, J. 36 1987 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060 Guckenheimer, John; Kuehn, Christian 35 2010 Computing slow manifolds of saddle type. Zbl 1176.37026 Guckenheimer, John; Kuehn, Christian 32 2009 Chaotic attractors of relaxation oscillators. Zbl 1102.34028 Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang 32 2006 Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007 Guckenheimer, J.; Labouriau, I. S. 31 1993 Shocks and rarefactions in two space dimensions. Zbl 0329.35043 Guckenheimer, John 30 1975 Numerical computation of canards. Zbl 0978.34038 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 30 2000 Computing Hopf bifurcations. I. Zbl 0948.37037 Guckenheimer, John; Myers, Mark; Sturmfels, Bernd 30 1997 Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075 Guckenheimer, John; Kuehn, Christian 28 2009 The forced van der Pol equation. II: Canards in the reduced system. Zbl 1089.37013 Bold, Katherine; Edwards, Chantal; Guckenheimer, John; Guharay, Sabyasachi; Hoffman, Kathleen; Hubbard, Judith; Oliva, Ricardo; Weckesser, Warren 28 2003 Integrability of plane quadratic vector fields. Zbl 0693.34030 Schlomiuk, Dana; Guckenheimer, John; Rand, Richard 24 1990 Multiple bifurcation problems of codimension two. Zbl 0543.34034 Guckenheimer, John 24 1984 Distortion of S-unimodal maps. Zbl 0708.58007 Guckenheimer, John; Johnson, Stewart 21 1990 A fast method for approximating invariant manifolds. Zbl 1059.37019 Guckenheimer, John; Vladimirsky, Alexander 20 2004 Dynamic models in biology. Zbl 1148.92001 Ellner, Stephen P.; Guckenheimer, John 20 2006 Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111 Guckenheimer, John; Meloon, Brian 19 2000 A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076 Guckenheimer, John; Scheper, Chris 19 2011 Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010 Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan 18 1997 Dynamics of the van der Pol equation. Zbl 0451.34045 Guckenheimer, John 17 1980 Catastrophes and partial differential equations. Zbl 0271.35006 Guckenheimer, John 16 1973 The duck and the devil: Canards on the staircase. Zbl 0985.34035 Guckenheimer, J.; Ilyashenko, Yu. 16 2001 Canards at folded nodes. Zbl 1092.34026 Guckenheimer, John; Haiduc, Radu 16 2005 Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027 Guckenheimer, John 16 1987 On a codimension two bifurcation. Zbl 0482.58006 Guckenheimer, John 16 1981 Random evolutionarily stable strategies. Zbl 0373.92017 Auslander, D.; Guckenheimer, J.; Oster, G. 15 1978 Multiple bifurcation problems for chemical reactors. Zbl 0593.34043 Guckenheimer, John 15 1986 Unfoldings of singular Hopf bifurcation. Zbl 1263.37083 Guckenheimer, John; Meerkamp, Philipp 15 2012 Bifurcations of dynamical systems. Zbl 0451.58025 Guckenheimer, John 14 1980 Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038 Guckenheimer, J.; Knobloch, E. 13 1983 Hartman’s theorem for complex flows in the Poincaré domain. Zbl 0239.58007 Guckenheimer, John 12 1972 Dissecting the phase response of a model bursting neuron. Zbl 1191.92011 Sherwood, William Erik; Guckenheimer, John 12 2010 The backward behavior of the Ricci and cross-curvature flows on SL\((2,\mathbb{R})\). Zbl 1198.53068 Cao, Xiaodong; Guckenheimer, John; Saloff-Coste, Laurent 12 2009 Instability induced by symmetry reduction. Zbl 1050.37516 Guckenheimer, J.; Mahalov, A. 11 1992 Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Zbl 0954.34032 Guckenheimer, John; Willms, Allan R. 11 2000 Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045 Guckenheimer, John 11 1995 Axiom A+NO cycles \(\to\zeta^ f(t)\) rational. Zbl 0196.27002 Guckenheimer, J. 10 1970 Absolutely \(\Omega\)-stable diffeomorphisms. Zbl 0246.58013 Guckenheimer, John 10 1972 Defining functions for multiple Hopf bifurcations. Zbl 0873.65053 Govaerts, W.; Guckenheimer, J.; Khibnik, A. 10 1997 Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038 Guckenheimer, John; Rand, Richard; Schlomiuk, Dana 10 1989 Invariant manifolds and global bifurcations. Zbl 1374.37076 Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn 9 2015 Empirical modelling of population time series data: The case of age and density dependent vital rates. Zbl 0451.92013 Brillinger, David R.; Guckenheimer, John; Guttorp, Peter; Oster, George 9 1980 An improved parameter estimation method for Hodgkin-Huxley models. Zbl 0927.92012 Willms, Allan R.; Baro, Deborah J.; Harris-Warrick, Ronald M.; Guckenheimer, John 9 1999 A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297 Guckenheimer, John 9 1995 Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 9 2005 Endomorphisms of the Riemann sphere. Zbl 0205.54102 Guckenheimer, J. 9 1970 Resonant triad interactions in symmetric systems. Zbl 0743.76029 Guckenheimer, John; Mahalov, Alex 9 1992 Instant chaos. Zbl 0765.58019 Guckenheimer, John; Worfolk, Patrick 9 1992 Computing periodic orbits with high accuracy. Zbl 0954.65092 Choe, Won Gyu; Guckenheimer, J. 8 1999 Persistent properties of bifurcations. Zbl 1194.37001 Guckenheimer, John 7 1983 The catastrophe controversy. Zbl 0407.58010 Guckenheimer, John 6 1978 Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016 Guckenheimer, John; Moser, Jürgen; Newhouse, Sheldon E. 6 1980 Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075 Guckenheimer, John; Myers, Mark 6 1996 Dimension estimates for attractors. Zbl 0584.58027 Guckenheimer, John 6 1984 Dynamical systems: Some computational problems. Zbl 0795.58034 Guckenheimer, John; Worfolk, Patrick 6 1993 Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065 Guckenheimer, John 6 1996 Symbolic dynamics and relaxation oscillations. Zbl 1194.37018 Guckenheimer, John 6 1980 Caustics and non-degenerate Hamiltonians. Zbl 0291.58010 Guckenheimer, John 5 1974 Solving a single conservation law. Zbl 0306.35020 Guckenheimer, John 5 1975 Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004 Golomb, David; Guckenheimer, John; Gueron, Shay 5 1993 Multiparameter bifurcation theory. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation (at Humboldt State University, Arcata, California). Zbl 0587.00009 5 1986 Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053 Guckenheimer, John; Tien, Joseph H.; Willms, Allan R. 5 2005 The bifurcation of quadratic functions. Zbl 0443.58017 Guckenheimer, John 4 1979 Shilnikov homoclinic bifurcation of mixed-mode oscillations. Zbl 1370.37038 Guckenheimer, John; Lizarraga, Ian 4 2015 Strange attractors in fluids: Another view. Zbl 0634.76058 Guckenheimer, John 4 1986 Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133 Guckenheimer, John; Malo, Salvador 4 1996 Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052 Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert 4 1991 The singular limit of a Hopf bifurcation. Zbl 1402.37060 Guckenheimer, John; Osinga, Hinke M. 4 2012 Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109 Guckenheimer, John; LaMar, M. Drew 4 2007 Using dynamical system tools in Matlab. Zbl 0958.65138 Choe, Won Gyu; Guckenheimer, J. 3 2000 Locomotion: exploiting noise for state estimation. Zbl 1411.92016 Guckenheimer, John; Javeed, Aurya 3 2019 Lateral stability of the spring-mass Hopper suggests a two-step control strategy for running. Zbl 1309.70030 Carver, Sean G.; Cowan, Noah J.; Guckenheimer, John M. 3 2009 Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036 Guckenheimer, John 3 2003 Rigorous enclosures of a slow manifold. Zbl 1260.34084 Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp 3 2012 One-parameter families of vector fields on two-manifolds: Another nondensity theorem. Zbl 0285.58007 Guckenheimer, John 2 1973 Numerical analysis of dynamical systems. Zbl 1034.37001 Guckenheimer, John 2 2002 Global bifurcations of periodic orbits in the forced Van der Pol equation. Zbl 1198.37085 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 2 2001 From data to dynamical systems. Zbl 1348.37044 Guckenheimer, John 2 2014 Patterns of bifurcation. Zbl 0498.58014 Guckenheimer, John 2 1980 Multiple time scale analysis of a model Belousov-Zhabotinskii reaction. Zbl 1284.34075 Guckenheimer, John; Scheper, Chris 2 2013 Dense lines of curvature on convex surfaces. Zbl 1443.53005 Guckenheimer, John 2 2020 Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator. Zbl 1446.92169 Sherwood, William Erik; Harris-Warrick, Ronald; Guckenheimer, John 2 2011 Dense lines of curvature on convex surfaces. Zbl 1443.53005 Guckenheimer, John 2 2020 Locomotion: exploiting noise for state estimation. Zbl 1411.92016 Guckenheimer, John; Javeed, Aurya 3 2019 Invariant manifolds and global bifurcations. Zbl 1374.37076 Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn 9 2015 Shilnikov homoclinic bifurcation of mixed-mode oscillations. Zbl 1370.37038 Guckenheimer, John; Lizarraga, Ian 4 2015 From data to dynamical systems. Zbl 1348.37044 Guckenheimer, John 2 2014 Flight stability of mosquitos: a reduced model. Zbl 1345.92025 Iams, Sarah; Guckenheimer, John 1 2014 Multiple time scale analysis of a model Belousov-Zhabotinskii reaction. Zbl 1284.34075 Guckenheimer, John; Scheper, Chris 2 2013 Mixed-mode oscillations with multiple time scales. Zbl 1250.34001 Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin 175 2012 Unfoldings of singular Hopf bifurcation. Zbl 1263.37083 Guckenheimer, John; Meerkamp, Philipp 15 2012 The singular limit of a Hopf bifurcation. Zbl 1402.37060 Guckenheimer, John; Osinga, Hinke M. 4 2012 Rigorous enclosures of a slow manifold. Zbl 1260.34084 Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp 3 2012 A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076 Guckenheimer, John; Scheper, Chris 19 2011 Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator. Zbl 1446.92169 Sherwood, William Erik; Harris-Warrick, Ronald; Guckenheimer, John 2 2011 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060 Guckenheimer, John; Kuehn, Christian 35 2010 Dissecting the phase response of a model bursting neuron. Zbl 1191.92011 Sherwood, William Erik; Guckenheimer, John 12 2010 Computing slow manifolds of saddle type. Zbl 1176.37026 Guckenheimer, John; Kuehn, Christian 32 2009 Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075 Guckenheimer, John; Kuehn, Christian 28 2009 The backward behavior of the Ricci and cross-curvature flows on SL\((2,\mathbb{R})\). Zbl 1198.53068 Cao, Xiaodong; Guckenheimer, John; Saloff-Coste, Laurent 12 2009 Lateral stability of the spring-mass Hopper suggests a two-step control strategy for running. Zbl 1309.70030 Carver, Sean G.; Cowan, Noah J.; Guckenheimer, John M. 3 2009 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025 Guckenheimer, John 55 2008 Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109 Guckenheimer, John; LaMar, M. Drew 4 2007 The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002 Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John 54 2006 Chaotic attractors of relaxation oscillators. Zbl 1102.34028 Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang 32 2006 Dynamic models in biology. Zbl 1148.92001 Ellner, Stephen P.; Guckenheimer, John 20 2006 A survey of methods for computing (un)stable manifolds of vector fields. Zbl 1086.34002 Krauskopf, B.; Osinga, H. M.; Doedel, E. J.; Henderson, M. E.; Guckenheimer, J.; Vladimirsky, A.; Dellnitz, M.; Junge, O. 92 2005 Canards at folded nodes. Zbl 1092.34026 Guckenheimer, John; Haiduc, Radu 16 2005 Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 9 2005 Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053 Guckenheimer, John; Tien, Joseph H.; Willms, Allan R. 5 2005 A fast method for approximating invariant manifolds. Zbl 1059.37019 Guckenheimer, John; Vladimirsky, Alexander 20 2004 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 48 2003 The forced van der Pol equation. II: Canards in the reduced system. Zbl 1089.37013 Bold, Katherine; Edwards, Chantal; Guckenheimer, John; Guharay, Sabyasachi; Hoffman, Kathleen; Hubbard, Judith; Oliva, Ricardo; Weckesser, Warren 28 2003 Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036 Guckenheimer, John 3 2003 Defining equations for bifurcations and singularities. Zbl 1050.37023 Guckenheimer, John; Xiang, Yongjian 1 2003 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005 Guckenheimer, John; Oliva, Ricardo A. 40 2002 Numerical analysis of dynamical systems. Zbl 1034.37001 Guckenheimer, John 2 2002 The duck and the devil: Canards on the staircase. Zbl 0985.34035 Guckenheimer, J.; Ilyashenko, Yu. 16 2001 Global bifurcations of periodic orbits in the forced Van der Pol equation. Zbl 1198.37085 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 2 2001 Computing periodic orbits. Zbl 1049.76048 Guckenheimer, John 1 2001 Numerical computation of canards. Zbl 0978.34038 Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 30 2000 Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111 Guckenheimer, John; Meloon, Brian 19 2000 Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Zbl 0954.34032 Guckenheimer, John; Willms, Allan R. 11 2000 Using dynamical system tools in Matlab. Zbl 0958.65138 Choe, Won Gyu; Guckenheimer, J. 3 2000 An improved parameter estimation method for Hodgkin-Huxley models. Zbl 0927.92012 Willms, Allan R.; Baro, Deborah J.; Harris-Warrick, Ronald M.; Guckenheimer, John 9 1999 Computing periodic orbits with high accuracy. Zbl 0954.65092 Choe, Won Gyu; Guckenheimer, J. 8 1999 Computing Hopf bifurcations. I. Zbl 0948.37037 Guckenheimer, John; Myers, Mark; Sturmfels, Bernd 30 1997 Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010 Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan 18 1997 Defining functions for multiple Hopf bifurcations. Zbl 0873.65053 Govaerts, W.; Guckenheimer, J.; Khibnik, A. 10 1997 Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075 Guckenheimer, John; Myers, Mark 6 1996 Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065 Guckenheimer, John 6 1996 Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133 Guckenheimer, John; Malo, Salvador 4 1996 Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045 Guckenheimer, John 11 1995 A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297 Guckenheimer, John 9 1995 Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007 Guckenheimer, J.; Labouriau, I. S. 31 1993 Dynamical systems: Some computational problems. Zbl 0795.58034 Guckenheimer, John; Worfolk, Patrick 6 1993 Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004 Golomb, David; Guckenheimer, John; Gueron, Shay 5 1993 Instability induced by symmetry reduction. Zbl 1050.37516 Guckenheimer, J.; Mahalov, A. 11 1992 Resonant triad interactions in symmetric systems. Zbl 0743.76029 Guckenheimer, John; Mahalov, Alex 9 1992 Instant chaos. Zbl 0765.58019 Guckenheimer, John; Worfolk, Patrick 9 1992 Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036 Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S. 76 1991 Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052 Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert 4 1991 Computational environments for exploring dynamical systems. Zbl 0874.58074 Guckenheimer, John 1 1991 Integrability of plane quadratic vector fields. Zbl 0693.34030 Schlomiuk, Dana; Guckenheimer, John; Rand, Richard 24 1990 Distortion of S-unimodal maps. Zbl 0708.58007 Guckenheimer, John; Johnson, Stewart 21 1990 Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036 Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 60 1989 Resonance regions for families of torus maps. Zbl 0678.58034 Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J. 41 1989 Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038 Guckenheimer, John; Rand, Richard; Schlomiuk, Dana 10 1989 Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027 Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 95 1988 Structurally stable heteroclinic cycles. Zbl 0645.58022 Guckenheimer, John; Holmes, Philip 89 1988 On a four parameter family of planar vector fields. Zbl 0654.34025 Dangelmayr, G.; Guckenheimer, J. 36 1987 Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027 Guckenheimer, John 16 1987 Multiple bifurcation problems for chemical reactors. Zbl 0593.34043 Guckenheimer, John 15 1986 Multiparameter bifurcation theory. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation (at Humboldt State University, Arcata, California). Zbl 0587.00009 5 1986 Strange attractors in fluids: Another view. Zbl 0634.76058 Guckenheimer, John 4 1986 A codimension two bifurcation with circular symmetry. Zbl 0616.58034 Guckenheimer, John 1 1986 Multiple bifurcation problems of codimension two. Zbl 0543.34034 Guckenheimer, John 24 1984 Dimension estimates for attractors. Zbl 0584.58027 Guckenheimer, John 6 1984 Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001 Guckenheimer, John; Holmes, Philip 3,929 1983 Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038 Guckenheimer, J.; Knobloch, E. 13 1983 Persistent properties of bifurcations. Zbl 1194.37001 Guckenheimer, John 7 1983 On a codimension two bifurcation. Zbl 0482.58006 Guckenheimer, John 16 1981 Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028 Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang 70 1980 Dynamics of the van der Pol equation. Zbl 0451.34045 Guckenheimer, John 17 1980 Bifurcations of dynamical systems. Zbl 0451.58025 Guckenheimer, John 14 1980 Empirical modelling of population time series data: The case of age and density dependent vital rates. Zbl 0451.92013 Brillinger, David R.; Guckenheimer, John; Guttorp, Peter; Oster, George 9 1980 Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016 Guckenheimer, John; Moser, Jürgen; Newhouse, Sheldon E. 6 1980 Symbolic dynamics and relaxation oscillations. Zbl 1194.37018 Guckenheimer, John 6 1980 Patterns of bifurcation. Zbl 0498.58014 Guckenheimer, John 2 1980 The growth of topological entropy for one dimensional maps. Zbl 0462.58022 Guckenheimer, John 1 1980 One-dimensional dynamics. Zbl 0482.58019 Guckenheimer, John 1 1980 Structural stability of Lorenz attractors. Zbl 0436.58018 Guckenheimer, John; Williams, R. F. 246 1979 Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012 Guckenheimer, John 183 1979 The bifurcation of quadratic functions. Zbl 0443.58017 Guckenheimer, John 4 1979 Random evolutionarily stable strategies. Zbl 0373.92017 Auslander, D.; Guckenheimer, J.; Oster, G. 15 1978 The catastrophe controversy. Zbl 0407.58010 Guckenheimer, John 6 1978 The dynamics of density dependent population models. Zbl 0379.92016 Guckenheimer, J.; Oster, G.; Ipaktchi, A. 153 1977 On the bifurcation of maps of the interval. Zbl 0354.58013 Guckenheimer, John 47 1977 The cusps of Zeeman’s catastrophe machine. Zbl 0354.58015 Guckenheimer, John 1 1977 The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale. Zbl 0346.58007 Marsden, J. E.; McCracken, M. 545 1976 Isochrons and phaseless sets. Zbl 0345.92001 Guckenheimer, J. 96 1975 Shocks and rarefactions in two space dimensions. Zbl 0329.35043 Guckenheimer, John 30 1975 ...and 11 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,955 Authors 65 Llibre, Jaume 54 Li, Jibin 50 Holmes, Philip J. 38 Kühn, Christian 37 Krauskopf, Bernd 37 Zhang, Weinian 36 Osinga, Hinke Maria 33 Yagasaki, Kazuyuki 32 Rodríguez-Luis, Alejandro J. 31 Algaba, Antonio 30 Knobloch, Edgar 29 Yu, Pei 28 Morales Rojas, Carlos Arnoldo 27 Ashwin, Peter 27 Jing, Zhujun 26 Chen, Guanrong 26 Guckenheimer, John M. 23 Wechselberger, Martin 23 Xu, Wei 22 Moehlis, Jeff 20 Desroches, Mathieu 20 Han, Maoan 20 Jiang, Weihua 19 Balasuriya, Sanjeeva 19 Bi, Qinsheng 19 Fečkan, Michal 19 Stewart, Ian Nicholas 18 Buonomo, Bruno 18 Feichtinger, Gustav 18 Wilson, Dan D. 17 Golubitsky, Martin A. 17 Yorke, James Alan 16 Barrio, Roberto 16 Chen, Hebai 16 Din, Qamar 16 Freire Macías, Emilio 16 Nusse, Helena Engelina 16 Rand, Richard H. 16 Zhang, Wei 15 Campbell, Sue Ann 15 Kuznetsov, Yuri Alexandrovich 15 Marsden, Jerrold Eldon 15 Melbourne, Ian 15 Piqueira, José Roberto Castilho 15 Rodrigues, Alexandre A. P. 15 Shen, Jianwei 14 Akhmet, Marat Ubaydulla 14 Bashkirtseva, Irina Adol’fovna 14 Broer, Henk W. 14 Gardini, Laura 14 Guo, Shangjiang 14 Krupa, Martin 14 Merino, Manuel 14 Ryashko, Lev Borisovich 14 Tang, Yilei 14 Wei, Junjie 13 Araújo, Vítor 13 Chung, Kwok-Wai 13 Haller, George 13 Labouriau, Isabel S. 13 Niu, Ben 13 Pacifico, Maria José 13 Postlethwaite, Claire M. 13 Xie, Jianhua 13 Young, Lai-Sang 12 Gamero, Estanislao 12 Kang, Yun 12 Kaper, Tasso J. 12 Mezić, Igor 12 Rubin, Jonathan E. 12 Teixeira, Marco Antonio 12 Valls Anglés, Cláudia 12 Yang, Qigui 11 Cao, Hongjun 11 Champneys, Alan R. 11 Doelman, Arjen 11 Govaerts, Willy J. F. 11 Huseyin, Koncay 11 Inaba, Naohiko 11 Jardón-Kojakhmetov, Hildeberto 11 Jiang, Guirong 11 Lacitignola, Deborah 11 Lyubich, Mikhail 11 MacKay, Robert Sinclair 11 Mireles-James, Jason D. 11 Palacios, Antonio 11 Rucklidge, Alastair M. 11 Saha, Asit Kumar 11 M-Seara, Tere 11 Tresser, Charles 11 Vo, Theodore 11 Wang, Qiudong 11 Wirl, Franz 11 Zgliczyński, Piotr 11 Zhu, Huaiping 10 Battelli, Flaviano 10 Chacón, Ricardo 10 Glass, Leon 10 Kirk, Vivien 10 Kloeden, Peter Eris ...and 6,855 more Authors all top 5 Cited in 524 Serials 476 Physica D 414 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 241 Chaos, Solitons and Fractals 196 Nonlinear Dynamics 155 Journal of Differential Equations 154 Chaos 116 Communications in Nonlinear Science and Numerical Simulation 115 Applied Mathematics and Computation 112 SIAM Journal on Applied Dynamical Systems 87 Journal of Mathematical Biology 79 Journal of Nonlinear Science 73 Journal of Mathematical Analysis and Applications 72 Physics Letters. 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Mathematical, Physical and Engineering Sciences 10 Geophysical and Astrophysical Fluid Dynamics 10 International Journal of Systems Science 10 Physics Reports 10 Theoretical Computer Science 10 Celestial Mechanics and Dynamical Astronomy 10 International Journal of Robust and Nonlinear Control 10 Journal of Mathematical Sciences (New York) ...and 424 more Serials all top 5 Cited in 62 Fields 2,772 Dynamical systems and ergodic theory (37-XX) 2,223 Ordinary differential equations (34-XX) 1,234 Biology and other natural sciences (92-XX) 591 Mechanics of particles and systems (70-XX) 587 Partial differential equations (35-XX) 437 Fluid mechanics (76-XX) 372 Systems theory; control (93-XX) 369 Numerical analysis (65-XX) 256 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 183 Difference and functional equations (39-XX) 147 Mechanics of deformable solids (74-XX) 134 Probability theory and stochastic processes (60-XX) 115 Computer science (68-XX) 102 General topology (54-XX) 100 Statistical mechanics, structure of matter (82-XX) 94 Global analysis, analysis on manifolds (58-XX) 91 Information and communication theory, circuits (94-XX) 68 Calculus of variations and optimal control; optimization (49-XX) 61 Measure and integration (28-XX) 54 Classical thermodynamics, heat transfer (80-XX) 54 Quantum theory (81-XX) 49 Optics, electromagnetic theory (78-XX) 46 Manifolds and cell complexes (57-XX) 46 Geophysics (86-XX) 43 Operator theory (47-XX) 40 Real functions (26-XX) 40 Operations research, mathematical programming (90-XX) 38 Statistics (62-XX) 37 Differential geometry (53-XX) 22 Functions of a complex variable (30-XX) 21 Combinatorics (05-XX) 20 Relativity and gravitational theory (83-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 15 History and biography (01-XX) 14 Several complex variables and analytic spaces (32-XX) 13 Integral equations (45-XX) 13 Astronomy and astrophysics (85-XX) 12 General and overarching topics; collections (00-XX) 11 Mathematical logic and foundations (03-XX) 11 Algebraic geometry (14-XX) 9 Topological groups, Lie groups (22-XX) 9 Special functions (33-XX) 9 Approximations and expansions (41-XX) 8 Commutative algebra (13-XX) 8 Functional analysis (46-XX) 7 Number theory (11-XX) 6 Field theory and polynomials (12-XX) 6 Group theory and generalizations (20-XX) 5 Associative rings and algebras (16-XX) 5 Nonassociative rings and algebras (17-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral transforms, operational calculus (44-XX) 4 Algebraic topology (55-XX) 4 Mathematics education (97-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Category theory; homological algebra (18-XX) 2 \(K\)-theory (19-XX) 2 Sequences, series, summability (40-XX) 2 Convex and discrete geometry (52-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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