PERIODIC SOLUTIONS AND SLOW MANIFOLDS-Reference-Cited by-同舟云学术

PERIODIC SOLUTIONS AND SLOW MANIFOLDS

Published:2007-08 Issue:08 Volume:17 Page:2533-2540
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

VERHULST FERDINAND¹

Affiliation:

1. Mathematisch Instituut, University of Utrecht, P. O. Box 80.010, 3508 TA Utrecht, The Netherlands

Abstract

After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we discuss a four-dimensional relaxation oscillation and also canard-like solutions emerging from the modified logistic equation with sign-alternating growth rates.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127407018609

Reference22 articles.

1. Dynamical Systems V

2. ON THE MODIFIED LOGISTIC EQUATION

3. Relaxation oscillations including a standard chase on French ducks

4. Persistence and Smoothness of Invariant Manifolds for Flows

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