On Pontryagin-Rodygin's theorem for convergence of solutions of slow and fast systems
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Date
2004-11-26
Authors
Sari, Tewfik
Yadi, Karim
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Singular perturbations, Asymptotic stability, Nonstandard analysis
Citation
Sari, T., & Yadi, K. (2004). On Pontryagin-Rodygin's theorem for convergence of solutions of slow and fast systems. <i>Electronic Journal of Differential Equations, 2004</i>(139), pp. 1-17.
Rights
Attribution 4.0 International