Book ChapterDOI
Geometric singular perturbation theory
Christopher K. R. T. Jones
- pp 44-118
Reads0
Chats0
About:
The article was published on 1995-01-01. It has received 1221 citations till now. The article focuses on the topics: Singular solution & Singular perturbation.read more
Citations
More filters
Journal ArticleDOI
The Dynamics of Legged Locomotion: Models, Analyses, and Challenges
TL;DR: This review describes mathematical models for legged animal locomotion, focusing on rapidly running insects and highlighting past achievements and challenges that remain.
Journal ArticleDOI
Mixed-Mode Oscillations with Multiple Time Scales
Mathieu Desroches,John Guckenheimer,Bernd Krauskopf,Christian Kuehn,Hinke M. Osinga,Martin Wechselberger +5 more
TL;DR: This survey of different types of MMOs is given, concentrating its analysis on MMOs whose small-amplitude oscillations are produced by a local, multiple-time-scale “mechanism.”
Journal ArticleDOI
Extending geometric singular perturbation theory to nonhyperbolic points—fold and canard points in two dimensions ∗
Martin Krupa,Peter Szmolyan +1 more
TL;DR: This work presents a method based on blow-up techniques, which leads to a rigorous geometric analysis of the extension of slow manifolds past fold points and canard points in planar systems.
Journal ArticleDOI
Relaxation Oscillation and Canard Explosion
Martin Krupa,Peter Szmolyan +1 more
TL;DR: In this paper, a geometric analysis of relaxation oscillations and canard cycles in singularly perturbed planar vector fields is presented. But the analysis is restricted to the case of singular cycles and does not consider the case where the transition from small Hopf-type cycles to large relaxation cycles occurs in an exponentially thin parameter interval.
Book ChapterDOI
Stability of Travelling Waves
TL;DR: In this paper, an overview of various aspects related to the spectral and nonlinear stability of travelling-wave solutions to partial differential equations is given, including the point and essential spectrum of the linearization about a travelling wave, the relation between these spectra, Fredholm properties, and the existence of exponential dichotomies for the linear operator.
References
More filters
Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Journal ArticleDOI