Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System*

Abstract

This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincaré map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.

Keywords

Singular perturbation / Subharmonic solution / Saddle-Node / Invariant torus / 34A26 / 34E15 / 34C25 / 34C29 / 34C45

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