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## Guckenheimer, John M.

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 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
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#### 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
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#### 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
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#### 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)

#### 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 0515.34001
Guckenheimer, John; Holmes, Philip
1983
Structural stability of Lorenz attractors. Zbl 0436.58018
Guckenheimer, John; Williams, R. F.
1979
Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012
Guckenheimer, John
1979
The dynamics of density dependent population models. Zbl 0379.92016
Guckenheimer, J.; Oster, G.; Ipaktchi, A.
1977
Mixed-mode oscillations with multiple time scales. Zbl 1250.34001
Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin
2012
Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
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.
2005
Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028
Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang
1980
Structurally stable heteroclinic cycles. Zbl 0645.58022
Guckenheimer, John; Holmes, Philip
1988
Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036
Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S.
1991
Isochrons and phaseless sets. Zbl 0345.92001
Guckenheimer, J.
1975
Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
1989
On the bifurcation of maps of the interval. Zbl 0354.58013
Guckenheimer, John
1977
Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025
Guckenheimer, John
2008
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
2006
The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
2003
Resonance regions for families of torus maps. Zbl 0678.58034
Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J.
1989
Chaos in the Hodgkin–Huxley model. Zbl 1002.92005
Guckenheimer, John; Oliva, Ricardo A.
2002
On a four parameter family of planar vector fields. Zbl 0654.34025
Dangelmayr, G.; Guckenheimer, J.
1987
Chaotic attractors of relaxation oscillators. Zbl 1102.34028
Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang
2006
Computing slow manifolds of saddle type. Zbl 1176.37026
Guckenheimer, John; Kuehn, Christian
2009
Computing Hopf bifurcations. I. Zbl 0948.37037
Guckenheimer, John; Myers, Mark; Sturmfels, Bernd
1997
Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007
Guckenheimer, J.; Labouriau, I. S.
1993
Multiple bifurcation problems of codimension two. Zbl 0543.34034
Guckenheimer, John
1984
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
2003
Shocks and rarefactions in two space dimensions. Zbl 0329.35043
Guckenheimer, John
1975
Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060
Guckenheimer, John; Kuehn, Christian
2010
Integrability of plane quadratic vector fields. Zbl 0693.34030
Schlomiuk, Dana; Guckenheimer, John; Rand, Richard
1990
Numerical computation of canards. Zbl 0978.34038
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
2000
Bifurcations of dynamical systems. Zbl 0451.58025
Guckenheimer, John
1980
A fast method for approximating invariant manifolds. Zbl 1059.37019
2004
Distortion of S-unimodal maps. Zbl 0708.58007
Guckenheimer, John; Johnson, Stewart
1990
Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111
Guckenheimer, John; Meloon, Brian
2000
Dynamic models in biology. Zbl 1148.92001
Ellner, Stephen P.; Guckenheimer, John
2006
Dynamics of the van der Pol equation. Zbl 0451.34045
Guckenheimer, John
1980
Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075
Guckenheimer, John; Kuehn, Christian
2009
Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010
Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan
1997
Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038
Guckenheimer, J.; Knobloch, E.
1983
Catastrophes and partial differential equations. Zbl 0271.35006
Guckenheimer, John
1973
Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027
Guckenheimer, John
1987
Multiple bifurcation problems for chemical reactors. Zbl 0593.34043
Guckenheimer, John
1986
Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016
Guckenheimer, John; Moser, Jürgen; Newhouse, Sheldon E.
1980
Random evolutionarily stable strategies. Zbl 0373.92017
Auslander, D.; Guckenheimer, J.; Oster, G.
1978
Canards at folded nodes. Zbl 1092.34026
2005
The duck and the devil: Canards on the staircase. Zbl 0985.34035
Guckenheimer, J.; Ilyashenko, Yu.
2001
On a codimension two bifurcation. Zbl 0482.58006
Guckenheimer, John
1981
Hartman’s theorem for complex flows in the Poincaré domain. Zbl 0239.58007
Guckenheimer, John
1972
Dissecting the phase response of a model bursting neuron. Zbl 1191.92011
Sherwood, William Erik; Guckenheimer, John
2010
Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Zbl 0954.34032
Guckenheimer, John; Willms, Allan R.
2000
Instability induced by symmetry reduction. Zbl 1050.37516
Guckenheimer, J.; Mahalov, A.
1992
A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076
Guckenheimer, John; Scheper, Chris
2011
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
2009
Defining functions for multiple Hopf bifurcations. Zbl 0873.65053
Govaerts, W.; Guckenheimer, J.; Khibnik, A.
1997
Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045
Guckenheimer, John
1995
Instant chaos. Zbl 0765.58019
Guckenheimer, John; Worfolk, Patrick
1992
Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038
Guckenheimer, John; Rand, Richard; Schlomiuk, Dana
1989
Absolutely $$\Omega$$-stable diffeomorphisms. Zbl 0246.58013
Guckenheimer, John
1972
Axiom A+NO cycles $$\to\zeta^ f(t)$$ rational. Zbl 0196.27002
Guckenheimer, J.
1970
Invariant manifolds and global bifurcations. Zbl 1374.37076
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn
2015
An improved parameter estimation method for Hodgkin-Huxley models. Zbl 0927.92012
Willms, Allan R.; Baro, Deborah J.; Harris-Warrick, Ronald M.; Guckenheimer, John
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 0587.00009
Golubitsky, Martin (ed.); Guckenheimer, John M. (ed.)
1986
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
1980
The bifurcation of quadratic functions. Zbl 0443.58017
Guckenheimer, John
1979
Endomorphisms of the Riemann sphere. Zbl 0205.54102
Guckenheimer, J.
1970
Unfoldings of singular Hopf bifurcation. Zbl 1263.37083
Guckenheimer, John; Meerkamp, Philipp
2012
Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
2005
Computing periodic orbits with high accuracy. Zbl 0954.65092
Choe, Won Gyu; Guckenheimer, J.
1999
A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297
Guckenheimer, John
1995
Resonant triad interactions in symmetric systems. Zbl 0743.76029
Guckenheimer, John; Mahalov, Alex
1992
Persistent properties of bifurcations. Zbl 1194.37001
Guckenheimer, John
1983
Dimension estimates for attractors. Zbl 0584.58027
Guckenheimer, John
1984
Symbolic dynamics and relaxation oscillations. Zbl 1194.37018
Guckenheimer, John
1980
Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075
Guckenheimer, John; Myers, Mark
1996
Dynamical systems: Some computational problems. Zbl 0795.58034
Guckenheimer, John; Worfolk, Patrick
1993
The catastrophe controversy. Zbl 0407.58010
Guckenheimer, John
1978
Caustics and non-degenerate Hamiltonians. Zbl 0291.58010
Guckenheimer, John
1974
Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133
1996
Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065
Guckenheimer, John
1996
Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004
Golomb, David; Guckenheimer, John; Gueron, Shay
1993
Strange attractors in fluids: Another view. Zbl 0634.76058
Guckenheimer, John
1986
Solving a single conservation law. Zbl 0306.35020
Guckenheimer, John
1975
The singular limit of a Hopf bifurcation. Zbl 1402.37060
Guckenheimer, John; Osinga, Hinke M.
2012
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.
2009
Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109
Guckenheimer, John; LaMar, M. Drew
2007
Using dynamical system tools in Matlab. Zbl 0958.65138
Choe, Won Gyu; Guckenheimer, J.
2000
A codimension two bifurcation with circular symmetry. Zbl 0616.58034
Guckenheimer, John
1986
Patterns of bifurcation. Zbl 0498.58014
Guckenheimer, John
1980
One-parameter families of vector fields on two-manifolds: Another nondensity theorem. Zbl 0285.58007
Guckenheimer, John
1973
From data to dynamical systems. Zbl 1348.37044
Guckenheimer, John
2014
Rigorous enclosures of a slow manifold. Zbl 1260.34084
Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp
2012
Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053
Guckenheimer, John; Tien, Joseph H.; Willms, Allan R.
2005
Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036
Guckenheimer, John
2003
Numerical analysis of dynamical systems. Zbl 1034.37001
Guckenheimer, John
2002
Global bifurcations of periodic orbits in the forced Van der Pol equation. Zbl 1198.37085
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
2001
Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052
Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert
1991
Bifurcation and catastrophe. Zbl 0287.58005
Guckenheimer, John
1973
Locomotion: exploiting noise for state estimation. Zbl 1411.92016
Guckenheimer, John; Javeed, Aurya
2019
Flight stability of mosquitos: a reduced model. Zbl 1345.92025
Iams, Sarah; Guckenheimer, John
2014
Multiple time scale analysis of a model Belousov-Zhabotinskii reaction. Zbl 1284.34075
Guckenheimer, John; Scheper, Chris
2013
Defining equations for bifurcations and singularities. Zbl 1050.37023
Guckenheimer, John; Xiang, Yongjian
2003
Locomotion: exploiting noise for state estimation. Zbl 1411.92016
Guckenheimer, John; Javeed, Aurya
2019
Invariant manifolds and global bifurcations. Zbl 1374.37076
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn
2015
From data to dynamical systems. Zbl 1348.37044
Guckenheimer, John
2014
Flight stability of mosquitos: a reduced model. Zbl 1345.92025
Iams, Sarah; Guckenheimer, John
2014
Multiple time scale analysis of a model Belousov-Zhabotinskii reaction. Zbl 1284.34075
Guckenheimer, John; Scheper, Chris
2013
Mixed-mode oscillations with multiple time scales. Zbl 1250.34001
Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin
2012
Unfoldings of singular Hopf bifurcation. Zbl 1263.37083
Guckenheimer, John; Meerkamp, Philipp
2012
The singular limit of a Hopf bifurcation. Zbl 1402.37060
Guckenheimer, John; Osinga, Hinke M.
2012
Rigorous enclosures of a slow manifold. Zbl 1260.34084
Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp
2012
A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076
Guckenheimer, John; Scheper, Chris
2011
Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060
Guckenheimer, John; Kuehn, Christian
2010
Dissecting the phase response of a model bursting neuron. Zbl 1191.92011
Sherwood, William Erik; Guckenheimer, John
2010
Computing slow manifolds of saddle type. Zbl 1176.37026
Guckenheimer, John; Kuehn, Christian
2009
Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075
Guckenheimer, John; Kuehn, Christian
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
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.
2009
Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025
Guckenheimer, John
2008
Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109
Guckenheimer, John; LaMar, M. Drew
2007
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
2006
Chaotic attractors of relaxation oscillators. Zbl 1102.34028
Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang
2006
Dynamic models in biology. Zbl 1148.92001
Ellner, Stephen P.; Guckenheimer, John
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.
2005
Canards at folded nodes. Zbl 1092.34026
2005
Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
2005
Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053
Guckenheimer, John; Tien, Joseph H.; Willms, Allan R.
2005
A fast method for approximating invariant manifolds. Zbl 1059.37019
2004
The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
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
2003
Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036
Guckenheimer, John
2003
Defining equations for bifurcations and singularities. Zbl 1050.37023
Guckenheimer, John; Xiang, Yongjian
2003
Chaos in the Hodgkin–Huxley model. Zbl 1002.92005
Guckenheimer, John; Oliva, Ricardo A.
2002
Numerical analysis of dynamical systems. Zbl 1034.37001
Guckenheimer, John
2002
The duck and the devil: Canards on the staircase. Zbl 0985.34035
Guckenheimer, J.; Ilyashenko, Yu.
2001
Global bifurcations of periodic orbits in the forced Van der Pol equation. Zbl 1198.37085
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
2001
Computing periodic orbits. Zbl 1049.76048
Guckenheimer, John
2001
Numerical computation of canards. Zbl 0978.34038
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
2000
Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111
Guckenheimer, John; Meloon, Brian
2000
Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Zbl 0954.34032
Guckenheimer, John; Willms, Allan R.
2000
Using dynamical system tools in Matlab. Zbl 0958.65138
Choe, Won Gyu; Guckenheimer, J.
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
1999
Computing periodic orbits with high accuracy. Zbl 0954.65092
Choe, Won Gyu; Guckenheimer, J.
1999
Computing Hopf bifurcations. I. Zbl 0948.37037
Guckenheimer, John; Myers, Mark; Sturmfels, Bernd
1997
Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010
Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan
1997
Defining functions for multiple Hopf bifurcations. Zbl 0873.65053
Govaerts, W.; Guckenheimer, J.; Khibnik, A.
1997
Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075
Guckenheimer, John; Myers, Mark
1996
Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133
1996
Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065
Guckenheimer, John
1996
Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045
Guckenheimer, John
1995
A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297
Guckenheimer, John
1995
Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007
Guckenheimer, J.; Labouriau, I. S.
1993
Dynamical systems: Some computational problems. Zbl 0795.58034
Guckenheimer, John; Worfolk, Patrick
1993
Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004
Golomb, David; Guckenheimer, John; Gueron, Shay
1993
Instability induced by symmetry reduction. Zbl 1050.37516
Guckenheimer, J.; Mahalov, A.
1992
Instant chaos. Zbl 0765.58019
Guckenheimer, John; Worfolk, Patrick
1992
Resonant triad interactions in symmetric systems. Zbl 0743.76029
Guckenheimer, John; Mahalov, Alex
1992
Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036
Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S.
1991
Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052
Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert
1991
Computational environments for exploring dynamical systems. Zbl 0874.58074
Guckenheimer, John
1991
Integrability of plane quadratic vector fields. Zbl 0693.34030
Schlomiuk, Dana; Guckenheimer, John; Rand, Richard
1990
Distortion of S-unimodal maps. Zbl 0708.58007
Guckenheimer, John; Johnson, Stewart
1990
Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
1989
Resonance regions for families of torus maps. Zbl 0678.58034
Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J.
1989
Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038
Guckenheimer, John; Rand, Richard; Schlomiuk, Dana
1989
Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
1988
Structurally stable heteroclinic cycles. Zbl 0645.58022
Guckenheimer, John; Holmes, Philip
1988
On a four parameter family of planar vector fields. Zbl 0654.34025
Dangelmayr, G.; Guckenheimer, J.
1987
Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027
Guckenheimer, John
1987
Multiple bifurcation problems for chemical reactors. Zbl 0593.34043
Guckenheimer, John
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
Golubitsky, Martin (ed.); Guckenheimer, John M. (ed.)
1986
Strange attractors in fluids: Another view. Zbl 0634.76058
Guckenheimer, John
1986
A codimension two bifurcation with circular symmetry. Zbl 0616.58034
Guckenheimer, John
1986
Multiple bifurcation problems of codimension two. Zbl 0543.34034
Guckenheimer, John
1984
Dimension estimates for attractors. Zbl 0584.58027
Guckenheimer, John
1984
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Zbl 0515.34001
Guckenheimer, John; Holmes, Philip
1983
Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038
Guckenheimer, J.; Knobloch, E.
1983
Persistent properties of bifurcations. Zbl 1194.37001
Guckenheimer, John
1983
On a codimension two bifurcation. Zbl 0482.58006
Guckenheimer, John
1981
Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028
Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang
1980
Bifurcations of dynamical systems. Zbl 0451.58025
Guckenheimer, John
1980
Dynamics of the van der Pol equation. Zbl 0451.34045
Guckenheimer, John
1980
Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016
Guckenheimer, John; Moser, Jürgen; Newhouse, Sheldon E.
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
1980
Symbolic dynamics and relaxation oscillations. Zbl 1194.37018
Guckenheimer, John
1980
Patterns of bifurcation. Zbl 0498.58014
Guckenheimer, John
1980
One-dimensional dynamics. Zbl 0482.58019
Guckenheimer, John
1980
The growth of topological entropy for one dimensional maps. Zbl 0462.58022
Guckenheimer, John
1980
Structural stability of Lorenz attractors. Zbl 0436.58018
Guckenheimer, John; Williams, R. F.
1979
Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012
Guckenheimer, John
1979
The bifurcation of quadratic functions. Zbl 0443.58017
Guckenheimer, John
1979
Random evolutionarily stable strategies. Zbl 0373.92017
Auslander, D.; Guckenheimer, J.; Oster, G.
1978
The catastrophe controversy. Zbl 0407.58010
Guckenheimer, John
1978
The dynamics of density dependent population models. Zbl 0379.92016
Guckenheimer, J.; Oster, G.; Ipaktchi, A.
1977
On the bifurcation of maps of the interval. Zbl 0354.58013
Guckenheimer, John
1977
Isochrons and phaseless sets. Zbl 0345.92001
Guckenheimer, J.
1975
Shocks and rarefactions in two space dimensions. Zbl 0329.35043
Guckenheimer, John
1975
Solving a single conservation law. Zbl 0306.35020
Guckenheimer, John
1975
Caustics and non-degenerate Hamiltonians. Zbl 0291.58010
Guckenheimer, John
1974
Caustics. Zbl 0304.58013
Guckenheimer, J.
1974
Catastrophes and partial differential equations. Zbl 0271.35006
Guckenheimer, John
1973
One-parameter families of vector fields on two-manifolds: Another nondensity theorem. Zbl 0285.58007
Guckenheimer, John
1973
...and 6 more Documents
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#### 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
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#### 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. Series A: Theory and Methods 52 Journal of Fluid Mechanics 50 Transactions of the American Mathematical Society 48 Nonlinear Analysis. Real World Applications 46 Journal of Computational and Applied Mathematics 46 Ergodic Theory and Dynamical Systems 46 Dynamics and Stability of Systems 42 Applied Mathematics and Mechanics. (English Edition) 40 Journal of Economic Dynamics & Control 39 Theoretical Population Biology 39 Journal of Theoretical Biology 39 Nonlinear Analysis. Theory, Methods & Applications 38 Automatica 37 Bulletin of Mathematical Biology 37 Proceedings of the American Mathematical Society 36 Mathematical and Computer Modelling 35 Biological Cybernetics 33 Journal of Difference Equations and Applications 33 Discrete Dynamics in Nature and Society 33 Dynamical Systems 32 Discrete and Continuous Dynamical Systems. Series B 30 Functional Analysis and its Applications 30 Physics of Fluids 28 ZAMP. Zeitschrift für angewandte Mathematik und Physik 28 Applied Mathematical Modelling 27 Computers & Mathematics with Applications 27 Systems & Control Letters 27 Acta Mathematicae Applicatae Sinica. English Series 27 Regular and Chaotic Dynamics 26 Journal of Mathematical Physics 25 Nonlinearity 25 Mathematical Problems in Engineering 25 Advances in Difference Equations 22 Qualitative Theory of Dynamical Systems 20 Topology and its Applications 20 Neural Computation 20 Journal of Computational Neuroscience 19 International Journal of Engineering Science 19 Physica A 18 Archive for Rational Mechanics and Analysis 18 Mathematical Methods in the Applied Sciences 18 Mathematics and Computers in Simulation 17 Advances in Mathematics 17 Acta Applicandae Mathematicae 17 The Journal of Mathematical Neuroscience 16 Journal of the Franklin Institute 16 International Journal of Circuit Theory and Applications 16 Applied Mathematics Letters 16 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 15 Journal of Computational Physics 15 Discrete and Continuous Dynamical Systems 14 Journal of Economic Theory 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Abstract and Applied Analysis 14 Journal of Biological Dynamics 13 Acta Mechanica 13 Computer Methods in Applied Mechanics and Engineering 13 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 13 Journal of Optimization Theory and Applications 13 Studies in Applied Mathematics 12 Theoretical Computer Science 11 Bulletin of the Australian Mathematical Society 11 International Journal of Control 11 Rocky Mountain Journal of Mathematics 11 Annales de l’Institut Fourier 11 Journal of Economics 11 Acta Mathematica Sinica. 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
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#### 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)

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