Tewfik Sari, Karim Yadi
Abstract:
In this paper we study fast and slow systems for which the fast
dynamics has limit cycles, for all fixed values of the slow variables.
The fundamental tool is the Pontryagin and Rodygin theorem which
describes the limiting behavior of the solutions in the continuously
differentiable case, when the cycles are exponentially stable.
We extend this result to the continuous case, and exponential
stability is replaced by asymptotic stability. We give two examples
with numerical simulations to illustrate the problem. Our results are
formulated in classical mathematics. They are proved using Nonstandard
Analysis.
Submitted May 12, 2004. Published November 26, 2004.
Math Subject Classifications: 34D15, 34E15, 34E18.
Key Words: Singular perturbations; asymptotic stability;
nonstandard analysis.
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| Tewfik Sari Laboratoire de Mathématiques et Applications Université de Haute Alsace 4, rue des frères Lumière 68093, Mulhouse, France email: Tewfik.Sari@uha.fr |
| Karim Yadi Laboratoire de Mathématiques et Applications Université de Haute Alsace 4, rue des frères Lumière 68093, Mulhouse, France email: K.Yadi@uha.fr |
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