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1

The Forced van der Pol Equation II: Canards in the Reduced System

Bold, Katherine, Edwards, Chantal, Guckenheimer, John, Guharay, Sabyasachi, Hoffman, Kathleen, Hubbard, Judith, Oliva, Ricardo, Weckesser, Warren

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2003

Language:

english

File:

PDF, 981 KB

english, 2003

2

The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations

Guckenheimer, John, Hoffman, Kathleen, Weckesser, Warren

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2003

Language:

english

File:

PDF, 1.06 MB

english, 2003

3

[Applied Mathematical Sciences] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Volume 42 ||

Guckenheimer, John, Holmes, Philip

Year:

1983

Language:

english

File:

PDF, 36.60 MB

english, 1983

4

The catastrophe controversy

John Guckenheimer

Journal:

The Mathematical Intelligencer

Year:

1978

Language:

english

File:

PDF, 1.89 MB

english, 1978

5

Structural stability of Lorenz attractors

John Guckenheimer, R. F. Williams

Journal:

Publications Mathématiques de L'IHÉS

Year:

1979

Language:

english

File:

PDF, 669 KB

english, 1979

6

Computing Slow Manifolds of Saddle Type

Guckenheimer, John, Kuehn, Christian

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2009

Language:

english

File:

PDF, 822 KB

english, 2009

7

Mixed-Mode Oscillations with Multiple Time Scales

Desroches, Mathieu, Guckenheimer, John, Krauskopf, Bernd, Kuehn, Christian, Osinga, Hinke M., Wechselberger, Martin

Journal:

Year:

2012

Language:

english

File:

PDF, 3.96 MB

english, 2012

8

Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry

Dieter Armbruster, John Guckenheimer, Philip Holmes

Journal:

Physica D: Nonlinear Phenomena

Year:

1988

Language:

english

File:

PDF, 1.35 MB

english, 1988

9

On the bifurcation of maps of the interval

John Guckenheimer

Journal:

Inventiones mathematicae

Year:

1977

Language:

english

File:

PDF, 884 KB

english, 1977

10

An Improved Parameter Estimation Method for Hodgkin-Huxley Models

Allan R. Willms, Deborah J. Baro, Ronald M. Harris-Warrick, John Guckenheimer

Journal:

Journal of Computational Neuroscience

Year:

1999

Language:

english

File:

PDF, 539 KB

english, 1999

11

Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold

Armbruster, Dieter, Guckenheimer, John, Holmes, Philip

Journal:

SIAM Journal on Applied Mathematics

Year:

1989

Language:

english

File:

PDF, 1.64 MB

english, 1989

12

Computing Periodic Orbits and their Bifurcations with Automatic Differentiation

Guckenheimer, John, Meloon, Brian

Journal:

SIAM Journal on Scientific Computing

Year:

2000

Language:

english

File:

PDF, 946 KB

english, 2000

13

Chaos in the Hodgkin--Huxley Model

Guckenheimer, John, Oliva, Ricardo A.

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2002

Language:

english

File:

PDF, 239 KB

english, 2002

14

Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System

Guckenheimer, John, Kuehn, Christian

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2010

Language:

english

File:

PDF, 455 KB

english, 2010

15

Kuramoto-Sivashinsky Dynamics on the Center-Unstable Manifold

Dieter Armbruster, John Guckenheimer and Philip Holmes

Journal:

SIAM Journal on Applied Mathematics

Year:

1989

Language:

english

File:

PDF, 1.22 MB

english, 1989

16

Stephen Smale: The Mathematician Who Broke the Dimension Barrierby Steve Batterson

Review by: John Guckenheimer

Journal:

American Mathematical Monthly

Year:

2001

Language:

english

File:

PDF, 160 KB

english, 2001

17

Distortion of S-Unimodal Maps

John Guckenheimer and Stewart Johnson

Journal:

Annals of Mathematics

Year:

1990

Language:

english

File:

PDF, 3.08 MB

english, 1990

18

Invariant manifolds and global bifurcations

Guckenheimer, John, Krauskopf, Bernd, Osinga, Hinke M., Sandstede, Björn

Journal:

Chaos An Interdisciplinary Journal of Nonlinear Science

Year:

2015

Language:

english

File:

PDF, 2.49 MB

english, 2015

19

Perspectives of Nonlinear Dynamics.by E. Atlee Jackson

Review by: John M. Guckenheimer

Journal:

American Mathematical Monthly

Year:

1990

Language:

english

File:

PDF, 353 KB

english, 1990

20

Absolutely Ω-stable diffeomorphisms

John Guckenheimer

Journal:

Year:

1972

Language:

english

File:

PDF, 157 KB

english, 1972

21

Caustics and non-degenerate Hamiltonians

John Guckenheimer

Journal:

Year:

1974

Language:

english

File:

PDF, 502 KB

english, 1974

22

The cusps of Zeeman's catastrophe machine

John Guckenheimer

Journal:

Year:

1977

Language:

english

File:

PDF, 349 KB

english, 1977

23

Symbolic dynamics and relaxation oscillations

John Guckenheimer

Journal:

Physica D: Nonlinear Phenomena

Year:

1980

Language:

english

File:

PDF, 648 KB

english, 1980

24

Chaotic dynamics in systems with square symmetry

Dieter Armbruster, John Guckenheimer, Seunghwan Kim

Journal:

Physics Letters A

Year:

1989

Language:

english

File:

PDF, 286 KB

english, 1989

25

Shocks and rarefactions in two space dimensions

John Guckenheimer

Journal:

Archive for Rational Mechanics and Analysis

Year:

1975

Language:

english

File:

PDF, 467 KB

english, 1975

26

Multiple Bifurcation Problems of Codimension Two

Guckenheimer, John

Journal:

SIAM Journal on Mathematical Analysis

Year:

1984

Language:

english

File:

PDF, 6.05 MB

english, 1984

27

Singular Hopf Bifurcation in Systems with Two Slow Variables

Guckenheimer, John

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2008

Language:

english

File:

PDF, 1.33 MB

english, 2008

28

A Fast Method for Approximating Invariant Manifolds

Guckenheimer, John, Vladimirsky, Alexander

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2004

Language:

english

File:

PDF, 1.17 MB

english, 2004

29

Unfoldings of Singular Hopf Bifurcation

Guckenheimer, John, Meerkamp, Philipp

Journal:

SIAM Journal on Applied Dynamical Systems

Year:

2012

Language:

english

File:

PDF, 1.60 MB

english, 2012

30

The Dynamics of Legged Locomotion: Models, Analyses, and Challenges

Philip Holmes, Robert J. Full, Dan Koditschek and John Guckenheimer

Journal:

Year:

2006

Language:

english

File:

PDF, 9.95 MB

english, 2006

31

Mapping the Dynamics of a Bursting Neuron

John Guckenheimer, Shay Gueron and Ronald M. Harris-Warrick

Journal:

Philosophical Transactions Biological Sciences

Year:

1993

Language:

english

File:

PDF, 1.91 MB

english, 1993

32

Computing Hopf Bifurcations I

John Guckenheimer, Mark Myers and Bernd Sturmfels

Journal:

SIAM Journal on Numerical Analysis

Year:

1997

Language:

english

File:

PDF, 1.79 MB

english, 1997

33

Chaotic attractors of relaxation oscillators

Guckenheimer, John, Wechselberger, Martin, Young, Lai-Sang

Journal:

Year:

2006

Language:

english

File:

PDF, 723 KB

english, 2006

34

Flight Stability of Mosquitos: A Reduced Model

Iams, Sarah, Guckenheimer, John

Journal:

SIAM Journal on Applied Mathematics

Year:

2014

Language:

english

File:

PDF, 483 KB

english, 2014

35

COMPUTATIONAL ENVIRONMENTS FOR EXPLORING DYNAMICAL SYSTEMS

GUCKENHEIMER, JOHN

Journal:

International Journal of Bifurcation and Chaos

Year:

1991

Language:

english

File:

PDF, 627 KB

english, 1991

36

DYNAMICAL SYSTEMS AND NUMERICAL ANALYSIS By A. M. STUART and A. R. HUMPHRIES Cambridge University Press, 1996, 709 pp. Price £40.00. ISBN 0 521 49672 1

GUCKENHEIMER, JOHN

Journal:

Ergodic Theory and Dynamical Systems

Year:

1998

Language:

english

File:

PDF, 28 KB

english, 1998

37

The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors.by Colin Sparrow

Review by: John Guckenheimer

Journal:

American Mathematical Monthly

Year:

1984

Language:

english

File:

PDF, 337 KB

english, 1984

38

Chaotic Transport in Dynamical Systems

Wiggins, Stephen, Guckenheimer, John

Journal:

Year:

1992

Language:

english

File:

PDF, 956 KB

english, 1992

39

The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors . By Colin Sparrow

Guckenheimer, John

Journal:

American Mathematical Monthly

Year:

1984

Language:

english

File:

PDF, 412 KB

english, 1984

40

The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors . By Colin Sparrow

Guckenheimer, John

Journal:

American Mathematical Monthly

Year:

1984

File:

PDF, 412 KB

1984

41

Persistent properties of bifurcations

John Guckenheimer

Journal:

Physica D: Nonlinear Phenomena

Year:

1983

Language:

english

File:

PDF, 456 KB

english, 1983

42

Multiple bifurcation problems for chemical reactors

John Guckenheimer

Journal:

Physica D: Nonlinear Phenomena

Year:

1986

Language:

english

File:

PDF, 1.77 MB

english, 1986

43

Resonant triad interactions in symmetric systems

John Guckenheimer, Alex Mahalov

Journal:

Physica D: Nonlinear Phenomena

Year:

1992

Language:

english

File:

PDF, 1.94 MB

english, 1992

44

Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport

Zhuyin Ren, Stephen B. Pope, Alexander Vladimirsky, John M. Guckenheimer

Journal:

Proceedings of the Combustion Institute

Year:

2007

Language:

english

File:

PDF, 225 KB

english, 2007

45

Asymptotic analysis of subcritical Hopf–homoclinic bifurcation

John Guckenheimer, Allan R. Willms

Journal:

Physica D: Nonlinear Phenomena

Year:

2000

Language:

english

File:

PDF, 367 KB

english, 2000

46

Reduction of a channel-based model for a stomatogastric ganglion LP neuron

David Golomb, John Guckenheimer, Shay Gueron

Journal:

Biological Cybernetics

Year:

1993

Language:

english

File:

PDF, 782 KB

english, 1993

47

Symmetry properties of confined convective states

John Guckenheimer

Journal:

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

Year:

1992

Language:

english

File:

PDF, 439 KB

english, 1992

48

Limit sets ofS-unimodal maps with zero entropy

John Guckenheimer

Journal:

Communications in Mathematical Physics

Year:

1987

Language:

english

File:

PDF, 313 KB

english, 1987

49

Sensitive dependence to initial conditions for one dimensional maps

John Guckenheimer

Journal:

Communications in Mathematical Physics

Year:

1979

Language:

english

File:

PDF, 2.32 MB

english, 1979

50

Parameter estimation for bursting neural models

Joseph H. Tien, John Guckenheimer

Journal:

Journal of Computational Neuroscience

Year:

2008

Language:

english

File:

PDF, 547 KB

english, 2008