Bifurcation from a homoclinic orbit in partial functional differential equations

Shigui Ruan, Junjie Wei, Jianhong Wu

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We consider a family of partial functional differential equations which has a homoclinic orbit asymptotic to an isolated equilibrium point at a critical value of the parameter. Under some technical assumptions, we show that a unique stable periodic orbit bifurcates from the homoclinic orbit. Our approach follows the ideas of Šil'nikov for ordinary differential equations and of Chow and Deng for semilinear parabolic equations and retarded functional differential equations.

Original languageEnglish (US)
Pages (from-to)1293-1322
Number of pages30
JournalDiscrete and Continuous Dynamical Systems
Volume9
Issue number5
DOIs
StatePublished - Sep 2003

Keywords

  • Bifurcation
  • Homoclinic orbit
  • Partial functional differential equations
  • Periodic solutions
  • Stable and unstable manifolds
  • Variation of constant formula

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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