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

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