Edit Profile Guckenheimer, John M. Compute Distance To: Compute Author ID: guckenheimer.john-m Published as: Guckenheimer, J.; Guckenheimer, John; Guckenheimer, John M. External Links: MGP · Wikidata · GND Documents Indexed: 126 Publications since 1970, including 4 Books Biographic References: 1 Publication all top 5 Co-Authors 55 single-authored 5 Hoffman, Kathleen A. 5 Holmes, Philip J. 5 Weckesser, Warren 4 Kühn, Christian 4 Osinga, Hinke Maria 4 Willms, Allan R. 3 Harris-Warrick, Ronald M. 3 Kim, Seunghwan 3 Krauskopf, Bernd 3 MacKay, Robert Sinclair 3 Oster, George F. 2 Armbruster, Dieter 2 Baesens, Claude 2 Choe, Won Gyu 2 Johnson, Stewart D. 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 Vladimirsky, Alexander 2 Wechselberger, Martin 2 Worfolk, Patrick A. 2 Young, Lai-Sang 1 Auslander, David M. 1 Baro, Deborah J. 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 Casey, Richard G. 1 Cohen, Itai 1 Cowan, Noah John 1 Dangelmayr, Gerhard 1 Dellnitz, Michael 1 Desroches, Mathieu 1 Doedel, Eusebius J. 1 Edwards, Chantal 1 Ellner, Stephen P. 1 Full, Robert J. 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 Hubbard, Judith 1 Iams, Sarah 1 Ilyashenko, Yulij Sergeevich 1 Ipaktchi, A. 1 Javeed, Aurya 1 Johnson, Tomas 1 Junge, Oliver 1 Khibnik, Alexander I. 1 Knobloch, Edgar 1 Koditschek, Dan 1 Labouriau, Isabel S. 1 Lamar, Michael Drew 1 Lizarraga, Ian 1 Malo, Salvador 1 Meloon, Brian 1 Misiurewicz, Michał 1 Moser, Jürgen K. 1 Newhouse, Sheldon E. 1 Peck, Jack 1 Phipps, Eric T. 1 Ristroph, Leif 1 Saloff-Coste, Laurent 1 Sandstede, Björn 1 Sturmfels, Bernd 1 Tien, Joseph H. 1 Wang, Z. Jane 1 Williams, Robert F. 1 Xiang, Yongjian 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 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 Experimental Mathematics 1 Communications in Analysis and Geometry 1 Discrete and Continuous Dynamical Systems 1 Annals of Mathematics. Second Series 1 Physical Review Letters 1 Bulletin of the American Mathematical Society 1 Applied Mathematical Sciences 1 Contemporary Mathematics 1 Progress in Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Anais da Academia Brasileira de Ciências all top 5 Fields 80 Dynamical systems and ergodic theory (37-XX) 43 Ordinary differential equations (34-XX) 26 Biology and other natural sciences (92-XX) 21 Numerical analysis (65-XX) 15 Global analysis, analysis on manifolds (58-XX) 7 Partial differential equations (35-XX) 7 Mechanics of particles and systems (70-XX) 7 Fluid mechanics (76-XX) 5 General topology (54-XX) 5 Systems theory; control (93-XX) 4 Differential geometry (53-XX) 3 General and overarching topics; collections (00-XX) 3 Manifolds and cell complexes (57-XX) 2 Measure and integration (28-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Computer science (68-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 106 Publications have been cited 6,002 times in 5,315 Documents Cited by ▼ Year ▼ Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001Guckenheimer, John; Holmes, Philip 3,796 1983 Structural stability of Lorenz attractors. Zbl 0436.58018Guckenheimer, John; Williams, R. F. 198 1979 Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012Guckenheimer, John 162 1979 The dynamics of density dependent population models. Zbl 0379.92016Guckenheimer, J.; Oster, G.; Ipaktchi, A. 146 1977 Mixed-mode oscillations with multiple time scales. Zbl 1250.34001Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin 116 2012 Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 90 1988 A survey of methods for computing (un)stable manifolds of vector fields. Zbl 1086.34002Krauskopf, B.; Osinga, H. M.; Doedel, E. J.; Henderson, M. E.; Guckenheimer, J.; Vladimirsky, A.; Dellnitz, M.; Junge, O. 78 2005 Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang 76 1980 Structurally stable heteroclinic cycles. Zbl 0645.58022Guckenheimer, John; Holmes, Philip 75 1988 Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S. 68 1991 Isochrons and phaseless sets. Zbl 0345.92001Guckenheimer, J. 66 1975 Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 50 1989 On the bifurcation of maps of the interval. Zbl 0354.58013Guckenheimer, John 46 1977 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025Guckenheimer, John 43 2008 The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John 42 2006 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 39 2003 Resonance regions for families of torus maps. Zbl 0678.58034Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J. 37 1989 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005Guckenheimer, John; Oliva, Ricardo A. 34 2002 On a four parameter family of planar vector fields. Zbl 0654.34025Dangelmayr, G.; Guckenheimer, J. 28 1987 Chaotic attractors of relaxation oscillators. Zbl 1102.34028Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang 27 2006 Computing slow manifolds of saddle type. Zbl 1176.37026Guckenheimer, John; Kuehn, Christian 26 2009 Computing Hopf bifurcations. I. Zbl 0948.37037Guckenheimer, John; Myers, Mark; Sturmfels, Bernd 25 1997 Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007Guckenheimer, J.; Labouriau, I. S. 25 1993 Multiple bifurcation problems of codimension two. Zbl 0543.34034Guckenheimer, John 25 1984 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 23 2003 Shocks and rarefactions in two space dimensions. Zbl 0329.35043Guckenheimer, John 23 1975 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060Guckenheimer, John; Kuehn, Christian 21 2010 Integrability of plane quadratic vector fields. Zbl 0693.34030Schlomiuk, Dana; Guckenheimer, John; Rand, Richard 21 1990 Numerical computation of canards. Zbl 0978.34038Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 20 2000 Bifurcations of dynamical systems. Zbl 0451.58025Guckenheimer, John 20 1980 A fast method for approximating invariant manifolds. Zbl 1059.37019Guckenheimer, John; Vladimirsky, Alexander 19 2004 Distortion of S-unimodal maps. Zbl 0708.58007Guckenheimer, John; Johnson, Stewart 19 1990 Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111Guckenheimer, John; Meloon, Brian 18 2000 Dynamic models in biology. Zbl 1148.92001Ellner, Stephen P.; Guckenheimer, John 17 2006 Dynamics of the van der Pol equation. Zbl 0451.34045Guckenheimer, John 17 1980 Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075Guckenheimer, John; Kuehn, Christian 16 2009 Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan 16 1997 Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038Guckenheimer, J.; Knobloch, E. 16 1983 Catastrophes and partial differential equations. Zbl 0271.35006Guckenheimer, John 16 1973 Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027Guckenheimer, John 15 1987 Multiple bifurcation problems for chemical reactors. Zbl 0593.34043Guckenheimer, John 14 1986 Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016Guckenheimer, John; Moser, Jürgen; Newhouse, Sheldon E. 14 1980 Random evolutionarily stable strategies. Zbl 0373.92017Auslander, D.; Guckenheimer, J.; Oster, G. 14 1978 Canards at folded nodes. Zbl 1092.34026Guckenheimer, John; Haiduc, Radu 13 2005 The duck and the devil: Canards on the staircase. Zbl 0985.34035Guckenheimer, J.; Ilyashenko, Yu. 12 2001 On a codimension two bifurcation. Zbl 0482.58006Guckenheimer, John 12 1981 Hartman’s theorem for complex flows in the Poincaré domain. Zbl 0239.58007Guckenheimer, John 12 1972 Dissecting the phase response of a model bursting neuron. Zbl 1191.92011Sherwood, William Erik; Guckenheimer, John 11 2010 Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Zbl 0954.34032Guckenheimer, John; Willms, Allan R. 11 2000 Instability induced by symmetry reduction. Zbl 1050.37516Guckenheimer, J.; Mahalov, A. 11 1992 A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076Guckenheimer, John; Scheper, Chris 10 2011 The backward behavior of the Ricci and cross-curvature flows on SL\((2,\mathbb{R})\). Zbl 1198.53068Cao, Xiaodong; Guckenheimer, John; Saloff-Coste, Laurent 10 2009 Defining functions for multiple Hopf bifurcations. Zbl 0873.65053Govaerts, W.; Guckenheimer, J.; Khibnik, A. 9 1997 Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045Guckenheimer, John 9 1995 Instant chaos. Zbl 0765.58019Guckenheimer, John; Worfolk, Patrick 9 1992 Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038Guckenheimer, John; Rand, Richard; Schlomiuk, Dana 9 1989 Absolutely \(\Omega\)-stable diffeomorphisms. Zbl 0246.58013Guckenheimer, John 9 1972 Axiom A+NO cycles \(\to\zeta^ f(t)\) rational. Zbl 0196.27002Guckenheimer, J. 9 1970 Invariant manifolds and global bifurcations. Zbl 1374.37076Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn 8 2015 An improved parameter estimation method for Hodgkin-Huxley models. Zbl 0927.92012Willms, Allan R.; Baro, Deborah J.; Harris-Warrick, Ronald M.; Guckenheimer, John 8 1999 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 0587.00009Golubitsky, Martin (ed.); Guckenheimer, John M. (ed.) 8 1986 Empirical modelling of population time series data: The case of age and density dependent vital rates. Zbl 0451.92013Brillinger, David R.; Guckenheimer, John; Guttorp, Peter; Oster, George 8 1980 The bifurcation of quadratic functions. Zbl 0443.58017Guckenheimer, John 8 1979 Endomorphisms of the Riemann sphere. Zbl 0205.54102Guckenheimer, J. 8 1970 Unfoldings of singular Hopf bifurcation. Zbl 1263.37083Guckenheimer, John; Meerkamp, Philipp 7 2012 Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 7 2005 Computing periodic orbits with high accuracy. Zbl 0954.65092Choe, Won Gyu; Guckenheimer, J. 7 1999 A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297Guckenheimer, John 7 1995 Resonant triad interactions in symmetric systems. Zbl 0743.76029Guckenheimer, John; Mahalov, Alex 7 1992 Persistent properties of bifurcations. Zbl 1194.37001Guckenheimer, John 7 1983 Dimension estimates for attractors. Zbl 0584.58027Guckenheimer, John 6 1984 Symbolic dynamics and relaxation oscillations. Zbl 1194.37018Guckenheimer, John 6 1980 Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075Guckenheimer, John; Myers, Mark 5 1996 Dynamical systems: Some computational problems. Zbl 0795.58034Guckenheimer, John; Worfolk, Patrick 5 1993 The catastrophe controversy. Zbl 0407.58010Guckenheimer, John 5 1978 Caustics and non-degenerate Hamiltonians. Zbl 0291.58010Guckenheimer, John 5 1974 Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133Guckenheimer, John; Malo, Salvador 4 1996 Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065Guckenheimer, John 4 1996 Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004Golomb, David; Guckenheimer, John; Gueron, Shay 4 1993 Strange attractors in fluids: Another view. Zbl 0634.76058Guckenheimer, John 4 1986 Solving a single conservation law. Zbl 0306.35020Guckenheimer, John 4 1975 The singular limit of a Hopf bifurcation. Zbl 1402.37060Guckenheimer, John; Osinga, Hinke M. 3 2012 Lateral stability of the spring-mass Hopper suggests a two-step control strategy for running. Zbl 1309.70030Carver, Sean G.; Cowan, Noah J.; Guckenheimer, John M. 3 2009 Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109Guckenheimer, John; LaMar, M. Drew 3 2007 Using dynamical system tools in Matlab. Zbl 0958.65138Choe, Won Gyu; Guckenheimer, J. 3 2000 A codimension two bifurcation with circular symmetry. Zbl 0616.58034Guckenheimer, John 3 1986 Patterns of bifurcation. Zbl 0498.58014Guckenheimer, John 3 1980 One-parameter families of vector fields on two-manifolds: Another nondensity theorem. Zbl 0285.58007Guckenheimer, John 3 1973 From data to dynamical systems. Zbl 1348.37044Guckenheimer, John 2 2014 Rigorous enclosures of a slow manifold. Zbl 1260.34084Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp 2 2012 Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053Guckenheimer, John; Tien, Joseph H.; Willms, Allan R. 2 2005 Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036Guckenheimer, John 2 2003 Numerical analysis of dynamical systems. Zbl 1034.37001Guckenheimer, John 2 2002 Global bifurcations of periodic orbits in the forced Van der Pol equation. Zbl 1198.37085Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 2 2001 Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert 2 1991 Bifurcation and catastrophe. Zbl 0287.58005Guckenheimer, John 2 1973 Locomotion: exploiting noise for state estimation. Zbl 1411.92016Guckenheimer, John; Javeed, Aurya 1 2019 Flight stability of mosquitos: a reduced model. Zbl 1345.92025Iams, Sarah; Guckenheimer, John 1 2014 Multiple time scale analysis of a model Belousov-Zhabotinskii reaction. Zbl 1284.34075Guckenheimer, John; Scheper, Chris 1 2013 Defining equations for bifurcations and singularities. Zbl 1050.37023Guckenheimer, John; Xiang, Yongjian 1 2003 Locomotion: exploiting noise for state estimation. Zbl 1411.92016Guckenheimer, John; Javeed, Aurya 1 2019 Invariant manifolds and global bifurcations. Zbl 1374.37076Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn 8 2015 From data to dynamical systems. Zbl 1348.37044Guckenheimer, John 2 2014 Flight stability of mosquitos: a reduced model. Zbl 1345.92025Iams, Sarah; Guckenheimer, John 1 2014 Multiple time scale analysis of a model Belousov-Zhabotinskii reaction. Zbl 1284.34075Guckenheimer, John; Scheper, Chris 1 2013 Mixed-mode oscillations with multiple time scales. Zbl 1250.34001Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin 116 2012 Unfoldings of singular Hopf bifurcation. Zbl 1263.37083Guckenheimer, John; Meerkamp, Philipp 7 2012 The singular limit of a Hopf bifurcation. Zbl 1402.37060Guckenheimer, John; Osinga, Hinke M. 3 2012 Rigorous enclosures of a slow manifold. Zbl 1260.34084Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp 2 2012 A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076Guckenheimer, John; Scheper, Chris 10 2011 Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060Guckenheimer, John; Kuehn, Christian 21 2010 Dissecting the phase response of a model bursting neuron. Zbl 1191.92011Sherwood, William Erik; Guckenheimer, John 11 2010 Computing slow manifolds of saddle type. Zbl 1176.37026Guckenheimer, John; Kuehn, Christian 26 2009 Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075Guckenheimer, John; Kuehn, Christian 16 2009 The backward behavior of the Ricci and cross-curvature flows on SL\((2,\mathbb{R})\). Zbl 1198.53068Cao, Xiaodong; Guckenheimer, John; Saloff-Coste, Laurent 10 2009 Lateral stability of the spring-mass Hopper suggests a two-step control strategy for running. Zbl 1309.70030Carver, Sean G.; Cowan, Noah J.; Guckenheimer, John M. 3 2009 Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025Guckenheimer, John 43 2008 Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109Guckenheimer, John; LaMar, M. Drew 3 2007 The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John 42 2006 Chaotic attractors of relaxation oscillators. Zbl 1102.34028Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang 27 2006 Dynamic models in biology. Zbl 1148.92001Ellner, Stephen P.; Guckenheimer, John 17 2006 A survey of methods for computing (un)stable manifolds of vector fields. Zbl 1086.34002Krauskopf, B.; Osinga, H. M.; Doedel, E. J.; Henderson, M. E.; Guckenheimer, J.; Vladimirsky, A.; Dellnitz, M.; Junge, O. 78 2005 Canards at folded nodes. Zbl 1092.34026Guckenheimer, John; Haiduc, Radu 13 2005 Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 7 2005 Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053Guckenheimer, John; Tien, Joseph H.; Willms, Allan R. 2 2005 A fast method for approximating invariant manifolds. Zbl 1059.37019Guckenheimer, John; Vladimirsky, Alexander 19 2004 The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 39 2003 The forced van der Pol equation. II: Canards in the reduced system. Zbl 1089.37013Bold, Katherine; Edwards, Chantal; Guckenheimer, John; Guharay, Sabyasachi; Hoffman, Kathleen; Hubbard, Judith; Oliva, Ricardo; Weckesser, Warren 23 2003 Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036Guckenheimer, John 2 2003 Defining equations for bifurcations and singularities. Zbl 1050.37023Guckenheimer, John; Xiang, Yongjian 1 2003 Chaos in the Hodgkin–Huxley model. Zbl 1002.92005Guckenheimer, John; Oliva, Ricardo A. 34 2002 Numerical analysis of dynamical systems. Zbl 1034.37001Guckenheimer, John 2 2002 The duck and the devil: Canards on the staircase. Zbl 0985.34035Guckenheimer, J.; Ilyashenko, Yu. 12 2001 Global bifurcations of periodic orbits in the forced Van der Pol equation. Zbl 1198.37085Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 2 2001 Computing periodic orbits. Zbl 1049.76048Guckenheimer, John 1 2001 Numerical computation of canards. Zbl 0978.34038Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren 20 2000 Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111Guckenheimer, John; Meloon, Brian 18 2000 Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Zbl 0954.34032Guckenheimer, John; Willms, Allan R. 11 2000 Using dynamical system tools in Matlab. Zbl 0958.65138Choe, Won Gyu; Guckenheimer, J. 3 2000 An improved parameter estimation method for Hodgkin-Huxley models. Zbl 0927.92012Willms, Allan R.; Baro, Deborah J.; Harris-Warrick, Ronald M.; Guckenheimer, John 8 1999 Computing periodic orbits with high accuracy. Zbl 0954.65092Choe, Won Gyu; Guckenheimer, J. 7 1999 Computing Hopf bifurcations. I. Zbl 0948.37037Guckenheimer, John; Myers, Mark; Sturmfels, Bernd 25 1997 Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan 16 1997 Defining functions for multiple Hopf bifurcations. Zbl 0873.65053Govaerts, W.; Guckenheimer, J.; Khibnik, A. 9 1997 Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075Guckenheimer, John; Myers, Mark 5 1996 Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133Guckenheimer, John; Malo, Salvador 4 1996 Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065Guckenheimer, John 4 1996 Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045Guckenheimer, John 9 1995 A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297Guckenheimer, John 7 1995 Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007Guckenheimer, J.; Labouriau, I. S. 25 1993 Dynamical systems: Some computational problems. Zbl 0795.58034Guckenheimer, John; Worfolk, Patrick 5 1993 Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004Golomb, David; Guckenheimer, John; Gueron, Shay 4 1993 Instability induced by symmetry reduction. Zbl 1050.37516Guckenheimer, J.; Mahalov, A. 11 1992 Instant chaos. Zbl 0765.58019Guckenheimer, John; Worfolk, Patrick 9 1992 Resonant triad interactions in symmetric systems. Zbl 0743.76029Guckenheimer, John; Mahalov, Alex 7 1992 Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S. 68 1991 Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert 2 1991 Computational environments for exploring dynamical systems. Zbl 0874.58074Guckenheimer, John 1 1991 Integrability of plane quadratic vector fields. Zbl 0693.34030Schlomiuk, Dana; Guckenheimer, John; Rand, Richard 21 1990 Distortion of S-unimodal maps. Zbl 0708.58007Guckenheimer, John; Johnson, Stewart 19 1990 Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 50 1989 Resonance regions for families of torus maps. Zbl 0678.58034Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J. 37 1989 Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038Guckenheimer, John; Rand, Richard; Schlomiuk, Dana 9 1989 Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027Armbruster, Dieter; Guckenheimer, John; Holmes, Philip 90 1988 Structurally stable heteroclinic cycles. Zbl 0645.58022Guckenheimer, John; Holmes, Philip 75 1988 On a four parameter family of planar vector fields. Zbl 0654.34025Dangelmayr, G.; Guckenheimer, J. 28 1987 Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027Guckenheimer, John 15 1987 Multiple bifurcation problems for chemical reactors. Zbl 0593.34043Guckenheimer, John 14 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 0587.00009Golubitsky, Martin (ed.); Guckenheimer, John M. (ed.) 8 1986 Strange attractors in fluids: Another view. Zbl 0634.76058Guckenheimer, John 4 1986 A codimension two bifurcation with circular symmetry. Zbl 0616.58034Guckenheimer, John 3 1986 Multiple bifurcation problems of codimension two. Zbl 0543.34034Guckenheimer, John 25 1984 Dimension estimates for attractors. Zbl 0584.58027Guckenheimer, John 6 1984 Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001Guckenheimer, John; Holmes, Philip 3,796 1983 Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038Guckenheimer, J.; Knobloch, E. 16 1983 Persistent properties of bifurcations. Zbl 1194.37001Guckenheimer, John 7 1983 On a codimension two bifurcation. Zbl 0482.58006Guckenheimer, John 12 1981 Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang 76 1980 Bifurcations of dynamical systems. Zbl 0451.58025Guckenheimer, John 20 1980 Dynamics of the van der Pol equation. Zbl 0451.34045Guckenheimer, John 17 1980 Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016Guckenheimer, John; Moser, Jürgen; Newhouse, Sheldon E. 14 1980 Empirical modelling of population time series data: The case of age and density dependent vital rates. Zbl 0451.92013Brillinger, David R.; Guckenheimer, John; Guttorp, Peter; Oster, George 8 1980 Symbolic dynamics and relaxation oscillations. Zbl 1194.37018Guckenheimer, John 6 1980 Patterns of bifurcation. Zbl 0498.58014Guckenheimer, John 3 1980 One-dimensional dynamics. Zbl 0482.58019Guckenheimer, John 1 1980 The growth of topological entropy for one dimensional maps. Zbl 0462.58022Guckenheimer, John 1 1980 Structural stability of Lorenz attractors. Zbl 0436.58018Guckenheimer, John; Williams, R. F. 198 1979 Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012Guckenheimer, John 162 1979 The bifurcation of quadratic functions. Zbl 0443.58017Guckenheimer, John 8 1979 Random evolutionarily stable strategies. Zbl 0373.92017Auslander, D.; Guckenheimer, J.; Oster, G. 14 1978 The catastrophe controversy. Zbl 0407.58010Guckenheimer, John 5 1978 The dynamics of density dependent population models. Zbl 0379.92016Guckenheimer, J.; Oster, G.; Ipaktchi, A. 146 1977 On the bifurcation of maps of the interval. Zbl 0354.58013Guckenheimer, John 46 1977 Isochrons and phaseless sets. Zbl 0345.92001Guckenheimer, J. 66 1975 Shocks and rarefactions in two space dimensions. Zbl 0329.35043Guckenheimer, John 23 1975 Solving a single conservation law. Zbl 0306.35020Guckenheimer, John 4 1975 Caustics and non-degenerate Hamiltonians. Zbl 0291.58010Guckenheimer, John 5 1974 Caustics. Zbl 0304.58013Guckenheimer, J. 1 1974 Catastrophes and partial differential equations. Zbl 0271.35006Guckenheimer, John 16 1973 One-parameter families of vector fields on two-manifolds: Another nondensity theorem. Zbl 0285.58007Guckenheimer, John 3 1973 ...and 6 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,672 Authors 63 Llibre, Jaume 57 Li, Jibin 53 Holmes, Philip J. 37 Yu, Pei 33 Knobloch, Edgar 33 Osinga, Hinke Maria 33 Zhang, Weinian 31 Jing, Zhujun 30 Krauskopf, Bernd 27 Chen, Guanrong 27 Rodríguez-Luis, Alejandro J. 24 Algaba, Antonio 24 Ashwin, Peter 24 Guckenheimer, John M. 24 Morales, Carlos Arnoldo 23 Kühn, Christian 23 Moehlis, Jeff 22 Han, Maoan 22 Wechselberger, Martin 22 Yagasaki, Kazuyuki 20 Xu, Wei 19 Feichtinger, Gustav 19 Jiang, Weihua 18 Balasuriya, Sanjeeva 18 Desroches, Mathieu 18 Golubitsky, Martin A. 18 Krupa, Martin 17 Fečkan, Michal 16 Barrio, Roberto 16 Freire Macías, Emilio 16 Nusse, Helena Engelina 16 Shen, Jianwei 16 Yang, Qigui 16 Yorke, James Alan 15 Buonomo, Bruno 15 Gardini, Laura 15 Kuznetsov, Yuri Alexandrovich 15 Melbourne, Ian 15 Stewart, Ian Nicholas 14 Haller, George 14 Marsden, Jerrold Eldon 14 Rand, Richard H. 14 Zhang, Wei 13 Akhmet, Marat Ubaydulla 13 Broer, Henk W. 13 Guo, Shangjiang 13 Labouriau, Isabel S. 13 Lacitignola, Deborah 13 Liu, Zhengrong 12 Campbell, Sue Ann 12 Cao, Hongjun 12 Kooi, Bob W. 12 Merino, Manuel 12 Piqueira, José Roberto Castilho 12 Teixeira, Marco Antonio 12 Wilson, Dan D. 12 Young, Lai-Sang 11 Champneys, Alan R. 11 Chen, Hebai 11 Chen, Lansun 11 Chung, Kwok-Wai 11 Gamero, Estanislao 11 Govaerts, Willy J. F. 11 Huseyin, Koncay 11 Kaper, Tasso J. 11 Kevrekidis, Ioannis George 11 Kirk, Vivien 11 Lyubich, Mikhail Yur’evich 11 Rinaldi, Sergio 11 M-Seara, Tere 11 Tang, Yilei 11 Tresser, Charles 11 Wei, Junjie 11 Wiggins, Stephen 11 Wirl, Franz 10 Bi, Qinsheng 10 Jiang, Guirong 10 Kang, Yun 10 Kar, Tapan Kumar 10 Kloeden, Peter Eris 10 Lenci, Stefano 10 Liu, Qian 10 Moiola, Jorge Luis 10 Niu, Ben 10 Pacifico, Maria José 10 Palacios, Antonio 10 Rodrigues, Alexandre A. P. 10 Rubin, Jonathan E. 10 Turaev, Dmitry V. 10 Vo, Theodore 10 Wang, Qiudong 10 Xie, Jianhua 10 Xu, Jian 10 Zgliczyński, Piotr 10 Zhang, Qingling 10 Zhou, Yuqian 10 Zhu, Huaiping 9 Aihara, Kazuyuki 9 Araújo, Vítor 9 Battelli, Flaviano ...and 6,572 more Authors all top 5 Cited in 447 Serials 523 Physica D 373 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 290 Chaos, Solitons and Fractals 179 Nonlinear Dynamics 149 Journal of Differential Equations 136 Chaos 132 Applied Mathematics and Computation 99 Communications in Nonlinear Science and Numerical Simulation 90 Journal of Mathematical Analysis and Applications 84 Physics Letters. A 73 Journal of Mathematical Biology 71 SIAM Journal on Applied Dynamical Systems 69 Journal of Nonlinear Science 62 Communications in Mathematical Physics 60 Journal of Statistical Physics 58 Mathematical Biosciences 56 Journal of Dynamics and Differential Equations 53 Nonlinear Analysis. Theory, Methods & Applications. 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English Series 11 Journal of Applied Analysis and Computation 10 International Journal of Modern Physics B 10 International Journal of Systems Science 10 Physics Reports 10 Reports on Mathematical Physics 10 Meccanica 10 Linear Algebra and its Applications 10 SIAM Journal on Applied Mathematics 10 Journal of Vibration and Control 9 Publications Mathématiques 9 Applied Numerical Mathematics 9 Bulletin of the American Mathematical Society. New Series 9 Celestial Mechanics and Dynamical Astronomy 9 International Journal of Robust and Nonlinear Control 9 European Journal of Mechanics. A. Solids 9 International Journal of Biomathematics ...and 347 more Serials all top 5 Cited in 61 Fields 2,654 Dynamical systems and ergodic theory (37-XX) 2,019 Ordinary differential equations (34-XX) 1,043 Biology and other natural sciences (92-XX) 551 Mechanics of particles and systems (70-XX) 531 Partial differential equations (35-XX) 416 Fluid mechanics (76-XX) 375 Systems theory; control (93-XX) 357 Numerical analysis (65-XX) 246 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 153 Mechanics of deformable solids (74-XX) 141 Difference and functional equations (39-XX) 111 General topology (54-XX) 111 Probability theory and stochastic processes (60-XX) 107 Computer science (68-XX) 92 Statistical mechanics, structure of matter (82-XX) 90 Global analysis, analysis on manifolds (58-XX) 83 Information and communication theory, circuits (94-XX) 59 Calculus of variations and optimal control; optimization (49-XX) 56 Measure and integration (28-XX) 51 Optics, electromagnetic theory (78-XX) 49 Classical thermodynamics, heat transfer (80-XX) 47 Quantum theory (81-XX) 45 Manifolds and cell complexes (57-XX) 42 Geophysics (86-XX) 40 Operations research, mathematical programming (90-XX) 38 Operator theory (47-XX) 35 Real functions (26-XX) 34 Statistics (62-XX) 32 Differential geometry (53-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 18 Relativity and gravitational theory (83-XX) 17 Combinatorics (05-XX) 17 Functions of a complex variable (30-XX) 13 History and biography (01-XX) 13 Several complex variables and analytic spaces (32-XX) 13 Integral equations (45-XX) 11 General and overarching topics; collections (00-XX) 10 Astronomy and astrophysics (85-XX) 9 Algebraic geometry (14-XX) 9 Topological groups, Lie groups (22-XX) 7 Approximations and expansions (41-XX) 7 Functional analysis (46-XX) 6 Mathematical logic and foundations (03-XX) 6 Number theory (11-XX) 6 Commutative algebra (13-XX) 6 Special functions (33-XX) 6 Algebraic topology (55-XX) 5 Field theory and polynomials (12-XX) 5 Nonassociative rings and algebras (17-XX) 5 Group theory and generalizations (20-XX) 5 Integral transforms, operational calculus (44-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Associative rings and algebras (16-XX) 4 Sequences, series, summability (40-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Convex and discrete geometry (52-XX) 2 Category theory; homological algebra (18-XX) 2 Mathematics education (97-XX) 1 \(K\)-theory (19-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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