Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Chiba, Hayato

关键词: Fast-slow system;    Blow up;    Singular perturbation;    Painleve equation;   

DOI  :  10.1016/j.jde.2010.09.022

来源: Elsevier

【 摘 要 】

The existence of stable periodic orbits and chaotic invariant sets of singularly perturbed problems of fast-slow type having Bogdanov-Takens bifurcation points in its fast subsystem is proved by means of the geometric singular perturbation method and the blow-up method In particular the blow-up method is effectively used for analyzing the flow near the Bogdanov-Takens type fold point in order to show that a slow manifold near the fold point is extended along the Boutroux s tritronquee solution of the first Painleve equation in the blow-up space (C) 2010 Elsevier Inc All rights reserved

【 授权许可】

Free