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Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields
TLDR
Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples. Expand
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The Dynamics of Legged Locomotion: Models, Analyses, and Challenges
TLDR
We describe mathematical models for legged animal locomotion, focusing on rapidly running insects and highlighting past achievements and challenges that remain. Expand
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Isochrons and phaseless sets
  • J. Guckenheimer
  • Mathematics, Medicine
  • Journal of mathematical biology
  • 1 September 1975
SummaryWinfree has developed mathematical models for his phase resetting experiments on biological clocks. These models lead him to ask a number of mathematical questions concerning dynamicalExpand
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Dynamic model
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Mixed-Mode Oscillations with Multiple Time Scales
Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small amplitudes. MMOs have been observed and studiedExpand
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Structurally stable heteroclinic cycles
This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of C r vector fieldsExpand
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Structural stability of Lorenz attractors
© Publications mathématiques de l’I.H.É.S., 1979, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
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Singular Hopf Bifurcation in Systems with Two Slow Variables
  • J. Guckenheimer
  • Computer Science, Mathematics
  • SIAM J. Appl. Dyn. Syst.
  • 31 October 2008
TLDR
Hopf bifurcations have been studied intensively in two dimensional vector fields with one slow and one fast variable [E. Krupa and P. Eckhaus, in Asymptotic Analysis II, Lecture Notes in Math. 137, Kluwer, Dordrecht, The Netherlands, 2004, pp. 295–316]. Expand
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