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

Brian A. Coomes, Hüseyin Koçak, Kenneth J. Palmer

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in Rnnear 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)
Pages (from-to)1081-1114
Number of pages34
JournalJournal of Dynamics and Differential Equations
Volume28
Issue number3-4
DOIs
StatePublished - Sep 1 2016

Keywords

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

ASJC Scopus subject areas

  • Analysis

Fingerprint

Dive into the research topics of 'A Computable Criterion for the Existence of Connecting Orbits in Autonomous Dynamics'. Together they form a unique fingerprint.

Cite this