×

zbMATH — the first resource for mathematics

Guckenheimer, John M.

Compute Distance To:
Author ID: guckenheimer.john-m Recent zbMATH articles by "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

Publications by Year

Citations contained in zbMATH Open

106 Publications have been cited 6,043 times in 5,354 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.
200
1979
Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012
Guckenheimer, John
162
1979
The dynamics of density dependent population models. Zbl 0379.92016
Guckenheimer, J.; Oster, G.; Ipaktchi, A.
146
1977
Mixed-mode oscillations with multiple time scales. Zbl 1250.34001
Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin
120
2012
Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
91
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.
78
2005
Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028
Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang
76
1980
Structurally stable heteroclinic cycles. Zbl 0645.58022
Guckenheimer, John; Holmes, Philip
75
1988
Isochrons and phaseless sets. Zbl 0345.92001
Guckenheimer, J.
69
1975
Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036
Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S.
68
1991
Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
51
1989
On the bifurcation of maps of the interval. Zbl 0354.58013
Guckenheimer, John
46
1977
Singular Hopf bifurcation in systems with two slow variables. Zbl 1168.37025
Guckenheimer, John
43
2008
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
43
2006
The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
39
2003
Resonance regions for families of torus maps. Zbl 0678.58034
Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J.
37
1989
Chaos in the Hodgkin–Huxley model. Zbl 1002.92005
Guckenheimer, John; Oliva, Ricardo A.
34
2002
On a four parameter family of planar vector fields. Zbl 0654.34025
Dangelmayr, G.; Guckenheimer, J.
28
1987
Computing slow manifolds of saddle type. Zbl 1176.37026
Guckenheimer, John; Kuehn, Christian
27
2009
Chaotic attractors of relaxation oscillators. Zbl 1102.34028
Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang
27
2006
Computing Hopf bifurcations. I. Zbl 0948.37037
Guckenheimer, John; Myers, Mark; Sturmfels, Bernd
25
1997
Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007
Guckenheimer, J.; Labouriau, I. S.
25
1993
Multiple bifurcation problems of codimension two. Zbl 0543.34034
Guckenheimer, John
25
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
23
2003
Shocks and rarefactions in two space dimensions. Zbl 0329.35043
Guckenheimer, John
23
1975
Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060
Guckenheimer, John; Kuehn, Christian
21
2010
Integrability of plane quadratic vector fields. Zbl 0693.34030
Schlomiuk, Dana; Guckenheimer, John; Rand, Richard
21
1990
Numerical computation of canards. Zbl 0978.34038
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
20
2000
Bifurcations of dynamical systems. Zbl 0451.58025
Guckenheimer, John
20
1980
A fast method for approximating invariant manifolds. Zbl 1059.37019
Guckenheimer, John; Vladimirsky, Alexander
19
2004
Distortion of S-unimodal maps. Zbl 0708.58007
Guckenheimer, John; Johnson, Stewart
19
1990
Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111
Guckenheimer, John; Meloon, Brian
18
2000
Dynamic models in biology. Zbl 1148.92001
Ellner, Stephen P.; Guckenheimer, John
17
2006
Dynamics of the van der Pol equation. Zbl 0451.34045
Guckenheimer, John
17
1980
Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075
Guckenheimer, John; Kuehn, Christian
16
2009
Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010
Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan
16
1997
Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038
Guckenheimer, J.; Knobloch, E.
16
1983
Catastrophes and partial differential equations. Zbl 0271.35006
Guckenheimer, John
16
1973
Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027
Guckenheimer, John
15
1987
Multiple bifurcation problems for chemical reactors. Zbl 0593.34043
Guckenheimer, John
14
1986
Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016
Guckenheimer, John; Moser, Jürgen; Newhouse, Sheldon E.
14
1980
Random evolutionarily stable strategies. Zbl 0373.92017
Auslander, D.; Guckenheimer, J.; Oster, G.
14
1978
Canards at folded nodes. Zbl 1092.34026
Guckenheimer, John; Haiduc, Radu
13
2005
The duck and the devil: Canards on the staircase. Zbl 0985.34035
Guckenheimer, J.; Ilyashenko, Yu.
12
2001
On a codimension two bifurcation. Zbl 0482.58006
Guckenheimer, John
12
1981
Hartman’s theorem for complex flows in the Poincaré domain. Zbl 0239.58007
Guckenheimer, John
12
1972
A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076
Guckenheimer, John; Scheper, Chris
11
2011
Dissecting the phase response of a model bursting neuron. Zbl 1191.92011
Sherwood, William Erik; Guckenheimer, John
11
2010
Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Zbl 0954.34032
Guckenheimer, John; Willms, Allan R.
11
2000
Instability induced by symmetry reduction. Zbl 1050.37516
Guckenheimer, J.; Mahalov, A.
11
1992
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
10
2009
Defining functions for multiple Hopf bifurcations. Zbl 0873.65053
Govaerts, W.; Guckenheimer, J.; Khibnik, A.
9
1997
Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045
Guckenheimer, John
9
1995
Instant chaos. Zbl 0765.58019
Guckenheimer, John; Worfolk, Patrick
9
1992
Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038
Guckenheimer, John; Rand, Richard; Schlomiuk, Dana
9
1989
Absolutely \(\Omega\)-stable diffeomorphisms. Zbl 0246.58013
Guckenheimer, John
9
1972
Axiom A+NO cycles \(\to\zeta^ f(t)\) rational. Zbl 0196.27002
Guckenheimer, J.
9
1970
Invariant manifolds and global bifurcations. Zbl 1374.37076
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn
8
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
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 0587.00009
Golubitsky, 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 0451.92013
Brillinger, David R.; Guckenheimer, John; Guttorp, Peter; Oster, George
8
1980
The bifurcation of quadratic functions. Zbl 0443.58017
Guckenheimer, John
8
1979
Endomorphisms of the Riemann sphere. Zbl 0205.54102
Guckenheimer, J.
8
1970
Unfoldings of singular Hopf bifurcation. Zbl 1263.37083
Guckenheimer, John; Meerkamp, Philipp
7
2012
Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
7
2005
Computing periodic orbits with high accuracy. Zbl 0954.65092
Choe, Won Gyu; Guckenheimer, J.
7
1999
A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297
Guckenheimer, John
7
1995
Resonant triad interactions in symmetric systems. Zbl 0743.76029
Guckenheimer, John; Mahalov, Alex
7
1992
Persistent properties of bifurcations. Zbl 1194.37001
Guckenheimer, John
7
1983
Dimension estimates for attractors. Zbl 0584.58027
Guckenheimer, John
6
1984
Symbolic dynamics and relaxation oscillations. Zbl 1194.37018
Guckenheimer, John
6
1980
Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075
Guckenheimer, John; Myers, Mark
5
1996
Dynamical systems: Some computational problems. Zbl 0795.58034
Guckenheimer, John; Worfolk, Patrick
5
1993
The catastrophe controversy. Zbl 0407.58010
Guckenheimer, John
5
1978
Caustics and non-degenerate Hamiltonians. Zbl 0291.58010
Guckenheimer, John
5
1974
Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133
Guckenheimer, John; Malo, Salvador
4
1996
Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065
Guckenheimer, John
4
1996
Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004
Golomb, David; Guckenheimer, John; Gueron, Shay
4
1993
Strange attractors in fluids: Another view. Zbl 0634.76058
Guckenheimer, John
4
1986
Solving a single conservation law. Zbl 0306.35020
Guckenheimer, John
4
1975
The singular limit of a Hopf bifurcation. Zbl 1402.37060
Guckenheimer, John; Osinga, Hinke M.
3
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.
3
2009
Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109
Guckenheimer, John; LaMar, M. Drew
3
2007
Using dynamical system tools in Matlab. Zbl 0958.65138
Choe, Won Gyu; Guckenheimer, J.
3
2000
A codimension two bifurcation with circular symmetry. Zbl 0616.58034
Guckenheimer, John
3
1986
Patterns of bifurcation. Zbl 0498.58014
Guckenheimer, John
3
1980
One-parameter families of vector fields on two-manifolds: Another nondensity theorem. Zbl 0285.58007
Guckenheimer, John
3
1973
From data to dynamical systems. Zbl 1348.37044
Guckenheimer, John
2
2014
Rigorous enclosures of a slow manifold. Zbl 1260.34084
Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp
2
2012
Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053
Guckenheimer, John; Tien, Joseph H.; Willms, Allan R.
2
2005
Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036
Guckenheimer, John
2
2003
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
Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052
Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert
2
1991
Bifurcation and catastrophe. Zbl 0287.58005
Guckenheimer, John
2
1973
Locomotion: exploiting noise for state estimation. Zbl 1411.92016
Guckenheimer, John; Javeed, Aurya
1
2019
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
1
2013
Defining equations for bifurcations and singularities. Zbl 1050.37023
Guckenheimer, John; Xiang, Yongjian
1
2003
Locomotion: exploiting noise for state estimation. Zbl 1411.92016
Guckenheimer, John; Javeed, Aurya
1
2019
Invariant manifolds and global bifurcations. Zbl 1374.37076
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M.; Sandstede, Björn
8
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
1
2013
Mixed-mode oscillations with multiple time scales. Zbl 1250.34001
Desroches, Mathieu; Guckenheimer, John; Krauskopf, Bernd; Kuehn, Christian; Osinga, Hinke M.; Wechselberger, Martin
120
2012
Unfoldings of singular Hopf bifurcation. Zbl 1263.37083
Guckenheimer, John; Meerkamp, Philipp
7
2012
The singular limit of a Hopf bifurcation. Zbl 1402.37060
Guckenheimer, John; Osinga, Hinke M.
3
2012
Rigorous enclosures of a slow manifold. Zbl 1260.34084
Guckenheimer, John; Johnson, Tomas; Meerkamp, Philipp
2
2012
A geometric model for mixed-mode oscillations in a chemical system. Zbl 1218.92076
Guckenheimer, John; Scheper, Chris
11
2011
Homoclinic orbits of the FitzHugh-Nagumo equation: bifurcations in the full system. Zbl 1210.34060
Guckenheimer, John; Kuehn, Christian
21
2010
Dissecting the phase response of a model bursting neuron. Zbl 1191.92011
Sherwood, William Erik; Guckenheimer, John
11
2010
Computing slow manifolds of saddle type. Zbl 1176.37026
Guckenheimer, John; Kuehn, Christian
27
2009
Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit. Zbl 1362.34075
Guckenheimer, John; Kuehn, Christian
16
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
10
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
43
2008
Periodic orbit continuation in multiple time scale systems. Zbl 1126.65109
Guckenheimer, John; LaMar, M. Drew
3
2007
The dynamics of legged locomotion: Models, analyses, and challenges. Zbl 1100.34002
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John
43
2006
Chaotic attractors of relaxation oscillators. Zbl 1102.34028
Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang
27
2006
Dynamic models in biology. Zbl 1148.92001
Ellner, Stephen P.; Guckenheimer, John
17
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.
78
2005
Canards at folded nodes. Zbl 1092.34026
Guckenheimer, John; Haiduc, Radu
13
2005
Bifurcations of relaxation oscillations near folded saddles. Zbl 1140.34368
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
7
2005
Bifurcations in the fast dynamics of neurons: implications for bursting. Zbl 1404.92053
Guckenheimer, John; Tien, Joseph H.; Willms, Allan R.
2
2005
A fast method for approximating invariant manifolds. Zbl 1059.37019
Guckenheimer, John; Vladimirsky, Alexander
19
2004
The forced van der Pol equation. I: The slow flow and its bifurcations. Zbl 1088.37504
Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
39
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
23
2003
Bifurcation and degenerate decomposition in multiple time scale dynamical systems. Zbl 1065.37036
Guckenheimer, John
2
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.
34
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.
12
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
20
2000
Computing periodic orbits and their bifurcations with automatic differentiation. Zbl 0976.65111
Guckenheimer, John; Meloon, Brian
18
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
8
1999
Computing periodic orbits with high accuracy. Zbl 0954.65092
Choe, Won Gyu; Guckenheimer, J.
7
1999
Computing Hopf bifurcations. I. Zbl 0948.37037
Guckenheimer, John; Myers, Mark; Sturmfels, Bernd
25
1997
Bifurcation, bursting, and spike frequency adaptation. Zbl 0888.92010
Guckenheimer, John; Harris-Warrick, Ronald; Peck, Jack; Willms, Allan
16
1997
Defining functions for multiple Hopf bifurcations. Zbl 0873.65053
Govaerts, W.; Guckenheimer, J.; Khibnik, A.
9
1997
Computing Hopf bifurcations. II: Three examples from neurophysiology. Zbl 0992.37075
Guckenheimer, John; Myers, Mark
5
1996
Computer-generated proofs of phase portraits for planar systems. Zbl 0882.68133
Guckenheimer, John; Malo, Salvador
4
1996
Towards a global theory of singularly perturbed dynamical systems. Zbl 0839.34065
Guckenheimer, John
4
1996
Phase portraits of planar vector fields: Computer proofs. Zbl 0856.34045
Guckenheimer, John
9
1995
A robust hybrid stabilization strategy for equilibria. Zbl 0825.93297
Guckenheimer, John
7
1995
Bifurcation of the Hodgkin and Huxley equations: A new twist. Zbl 0778.92007
Guckenheimer, J.; Labouriau, I. S.
25
1993
Dynamical systems: Some computational problems. Zbl 0795.58034
Guckenheimer, John; Worfolk, Patrick
5
1993
Reduction of a channel-based model for a stomatogastric ganglion LP neuron. Zbl 0773.92004
Golomb, David; Guckenheimer, John; Gueron, Shay
4
1993
Instability induced by symmetry reduction. Zbl 1050.37516
Guckenheimer, J.; Mahalov, A.
11
1992
Instant chaos. Zbl 0765.58019
Guckenheimer, John; Worfolk, Patrick
9
1992
Resonant triad interactions in symmetric systems. Zbl 0743.76029
Guckenheimer, John; Mahalov, Alex
7
1992
Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos. Zbl 0734.58036
Baesens, C.; Guckenheimer, J.; Kim, S.; MacKay, R. S.
68
1991
Simple resonance regions of torus diffeomorphisms. Zbl 0744.58052
Baesens, Claude; Guckenheimer, John; Kim, Seunghwan; MacKay, Robert
2
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
21
1990
Distortion of S-unimodal maps. Zbl 0708.58007
Guckenheimer, John; Johnson, Stewart
19
1990
Kuramoto-Sivashinsky dynamics on the center-unstable manifold. Zbl 0687.34036
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
51
1989
Resonance regions for families of torus maps. Zbl 0678.58034
Kim, Seunghwan; MacKay, R. S.; Guckenheimer, J.
37
1989
Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038
Guckenheimer, John; Rand, Richard; Schlomiuk, Dana
9
1989
Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. Zbl 0634.34027
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip
91
1988
Structurally stable heteroclinic cycles. Zbl 0645.58022
Guckenheimer, John; Holmes, Philip
75
1988
On a four parameter family of planar vector fields. Zbl 0654.34025
Dangelmayr, G.; Guckenheimer, J.
28
1987
Limit sets of S-unimodal maps with zero entropy. Zbl 0625.58027
Guckenheimer, John
15
1987
Multiple bifurcation problems for chemical reactors. Zbl 0593.34043
Guckenheimer, 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 0587.00009
Golubitsky, Martin (ed.); Guckenheimer, John M. (ed.)
8
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
3
1986
Multiple bifurcation problems of codimension two. Zbl 0543.34034
Guckenheimer, John
25
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
1983
Nonlinear convection in a rotating layer: Amplitude expansions and normal forms. Zbl 0527.76038
Guckenheimer, J.; Knobloch, E.
16
1983
Persistent properties of bifurcations. Zbl 1194.37001
Guckenheimer, John
7
1983
On a codimension two bifurcation. Zbl 0482.58006
Guckenheimer, John
12
1981
Periodic points and topological entropy of one dimensional maps. Zbl 0447.58028
Block, Louis; Guckenheimer, John; Misiurewicz, Michal; Young, Lai Sang
76
1980
Bifurcations of dynamical systems. Zbl 0451.58025
Guckenheimer, John
20
1980
Dynamics of the van der Pol equation. Zbl 0451.34045
Guckenheimer, John
17
1980
Dynamical systems. C.I.M.E. Lectures, Bressanone, Italy, June 1978. Zbl 0431.00016
Guckenheimer, 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 0451.92013
Brillinger, David R.; Guckenheimer, John; Guttorp, Peter; Oster, George
8
1980
Symbolic dynamics and relaxation oscillations. Zbl 1194.37018
Guckenheimer, John
6
1980
Patterns of bifurcation. Zbl 0498.58014
Guckenheimer, John
3
1980
One-dimensional dynamics. Zbl 0482.58019
Guckenheimer, John
1
1980
The growth of topological entropy for one dimensional maps. Zbl 0462.58022
Guckenheimer, John
1
1980
Structural stability of Lorenz attractors. Zbl 0436.58018
Guckenheimer, John; Williams, R. F.
200
1979
Sensitive dependence to initial conditions for one dimensional maps. Zbl 0429.58012
Guckenheimer, John
162
1979
The bifurcation of quadratic functions. Zbl 0443.58017
Guckenheimer, John
8
1979
Random evolutionarily stable strategies. Zbl 0373.92017
Auslander, D.; Guckenheimer, J.; Oster, G.
14
1978
The catastrophe controversy. Zbl 0407.58010
Guckenheimer, John
5
1978
The dynamics of density dependent population models. Zbl 0379.92016
Guckenheimer, J.; Oster, G.; Ipaktchi, A.
146
1977
On the bifurcation of maps of the interval. Zbl 0354.58013
Guckenheimer, John
46
1977
Isochrons and phaseless sets. Zbl 0345.92001
Guckenheimer, J.
69
1975
Shocks and rarefactions in two space dimensions. Zbl 0329.35043
Guckenheimer, John
23
1975
Solving a single conservation law. Zbl 0306.35020
Guckenheimer, John
4
1975
Caustics and non-degenerate Hamiltonians. Zbl 0291.58010
Guckenheimer, John
5
1974
Caustics. Zbl 0304.58013
Guckenheimer, J.
1
1974
Catastrophes and partial differential equations. Zbl 0271.35006
Guckenheimer, John
16
1973
One-parameter families of vector fields on two-manifolds: Another nondensity theorem. Zbl 0285.58007
Guckenheimer, John
3
1973
...and 6 more Documents
all top 5

Cited by 6,727 Authors

64 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
29 Rodríguez-Luis, Alejandro J.
27 Chen, Guanrong
26 Algaba, Antonio
24 Ashwin, Peter
24 Guckenheimer, John M.
24 Morales, Carlos Arnoldo
23 Kühn, Christian
23 Moehlis, Jeff
23 Yagasaki, Kazuyuki
22 Han, Maoan
22 Wechselberger, Martin
20 Jiang, Weihua
20 Xu, Wei
19 Desroches, Mathieu
19 Feichtinger, Gustav
19 Krupa, Martin
18 Balasuriya, Sanjeeva
18 Golubitsky, Martin A.
17 Barrio, Roberto
17 Fečkan, Michal
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
15 Zhang, Wei
14 Haller, George
14 Marsden, Jerrold Eldon
14 Rand, Richard H.
13 Akhmet, Marat Ubaydulla
13 Broer, Henk W.
13 Chung, Kwok-Wai
13 Guo, Shangjiang
13 Labouriau, Isabel S.
13 Lacitignola, Deborah
13 Liu, Zhengrong
13 Wilson, Dan D.
12 Campbell, Sue Ann
12 Cao, Hongjun
12 Kooi, Bob W.
12 Merino, Manuel
12 Piqueira, José Roberto Castilho
12 Teixeira, Marco Antonio
12 Young, Lai-Sang
11 Champneys, Alan R.
11 Chen, Hebai
11 Chen, Lansun
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 Philippe
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 Mezić, Igor
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
...and 6,627 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
181 Nonlinear Dynamics
149 Journal of Differential Equations
146 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
76 SIAM Journal on Applied Dynamical Systems
73 Journal of Mathematical Biology
73 Journal of Nonlinear Science
62 Communications in Mathematical Physics
60 Journal of Statistical Physics
58 Mathematical Biosciences
56 Journal of Dynamics and Differential Equations
54 Journal of Fluid Mechanics
53 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
50 Transactions of the American Mathematical Society
49 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 Automatica
39 Theoretical Population Biology
39 Journal of Theoretical Biology
39 Nonlinear Analysis. Theory, Methods & Applications
37 Bulletin of Mathematical Biology
37 Proceedings of the American Mathematical Society
36 Mathematical and Computer Modelling
35 Biological Cybernetics
35 Discrete Dynamics in Nature and Society
33 Journal of Difference Equations and Applications
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
28 Mathematical Problems in Engineering
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 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
14 Journal of Applied Analysis and Computation
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
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
10 International Journal of Biomathematics
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
...and 347 more Serials
all top 5

Cited in 61 Fields

2,678 Dynamical systems and ergodic theory (37-XX)
2,036 Ordinary differential equations (34-XX)
1,054 Biology and other natural sciences (92-XX)
551 Mechanics of particles and systems (70-XX)
536 Partial differential equations (35-XX)
420 Fluid mechanics (76-XX)
376 Systems theory; control (93-XX)
359 Numerical analysis (65-XX)
247 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
153 Mechanics of deformable solids (74-XX)
145 Difference and functional equations (39-XX)
111 General topology (54-XX)
110 Probability theory and stochastic processes (60-XX)
108 Computer science (68-XX)
90 Global analysis, analysis on manifolds (58-XX)
89 Statistical mechanics, structure of matter (82-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)
51 Classical thermodynamics, heat transfer (80-XX)
47 Quantum theory (81-XX)
45 Manifolds and cell complexes (57-XX)
43 Geophysics (86-XX)
40 Operations research, mathematical programming (90-XX)
38 Operator theory (47-XX)
35 Real functions (26-XX)
34 Statistics (62-XX)
31 Differential geometry (53-XX)
19 Linear and multilinear algebra; matrix theory (15-XX)
18 Combinatorics (05-XX)
18 Relativity and gravitational theory (83-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)
12 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)
8 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)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Convex and discrete geometry (52-XX)
2 Category theory; homological algebra (18-XX)
2 Sequences, series, summability (40-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. Updates and corrections should be made in Wikidata.