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

Hayato Chiba

Research output: Contribution to journalArticle

18 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 - Jan 1 2011

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Slow-fast System
Chaos theory
Periodic Orbits
Blow-up
Chaos
Orbits
Fold
Bogdanov-Takens Bifurcation
Slow Manifold
Singular Perturbation Method
Singularly Perturbed Problem
Bifurcation Point
Invariant Set
Subsystem

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points. / Chiba, Hayato.

In: Journal of Differential Equations, Vol. 250, No. 1, 01.01.2011, p. 112-160.

Research output: Contribution to journalArticle

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