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

Brian A Coomes; Huseyin Kocak; Kenneth J. Palmer

doi:10.1007/s10884-015-9437-y

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

Brian A Coomes, Huseyin Kocak, Kenneth J. Palmer

Research output: Contribution to journal › Article

2 Scopus citations

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 language	English (US)
Journal	Journal of Dynamics and Differential Equations
DOIs	https://doi.org/10.1007/s10884-015-9437-y
State	Accepted/In press - Mar 5 2015

Keywords

Approximate orbits
Chaos
Connecting orbits
Heteroclinic cycle
Homoclinic orbits

ASJC Scopus subject areas

Analysis

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10.1007/s10884-015-9437-y

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Coomes, B. A., Kocak, H., & Palmer, K. J. (Accepted/In press). A Computable Criterion for the Existence of Connecting Orbits in Autonomous Dynamics. Journal of Dynamics and Differential Equations. https://doi.org/10.1007/s10884-015-9437-y

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