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

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19 Citations (Scopus)

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 tritronquée solution of the first Painlevé equation in the blow-up space.

Original languageEnglish
Pages (from-to)112-160
Number of pages49
JournalJournal of Differential Equations
Volume250
Issue number1
DOIs
Publication statusPublished - 2011 Jan 1

Keywords

  • Blow-up
  • Fast-slow system
  • Painlevé equation
  • Singular perturbation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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