A Computable Criterion for the Existence of Connecting Orbits in Autonomous Dynamics

Brian A Coomes, Huseyin Kocak, Kenneth J. Palmer

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in (Formula presented.) near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of the theorem is described using five examples including two Sil’nikov saddle-focus homoclinic orbits and a Sil’nikov saddle-focus heteroclinic cycle.

Original languageEnglish (US)
JournalJournal of Dynamics and Differential Equations
DOIs
StateAccepted/In press - Mar 5 2015

Fingerprint

Connecting Orbits
Saddle
Heteroclinic Cycle
Homoclinic Orbit
Invertibility
Theorem
Differential equation

Keywords

  • Approximate orbits
  • Chaos
  • Connecting orbits
  • Heteroclinic cycle
  • Homoclinic orbits

ASJC Scopus subject areas

  • Analysis

Cite this

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AB - A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in (Formula presented.) near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of the theorem is described using five examples including two Sil’nikov saddle-focus homoclinic orbits and a Sil’nikov saddle-focus heteroclinic cycle.

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