Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points
Dynamical Systems
2015-03-13 v3
Abstract
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 tritronqu\'{e}e solution of the first Painlev\'{e} equation in the blow-up space.
Keywords
Cite
@article{arxiv.0812.1446,
title = {Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points},
author = {Hayato Chiba},
journal= {arXiv preprint arXiv:0812.1446},
year = {2015}
}