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

A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in R n near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of...

Full description

Saved in:
Bibliographic Details
Published inJournal of dynamics and differential equations Vol. 28; no. 3-4; pp. 1081 - 1114
Main Authors Coomes, Brian A., Koçak, Hüseyin, Palmer, Kenneth J.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2016
Springer Nature B.V
Subjects
Applications of Mathematics
Differential equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Heteroclinic cycle
Chaos
58F13
Approximate orbits
Connecting orbits
58F22
Homoclinic orbits
65H10
Online AccessGet full text

Cover

More Information
Summary:A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in R n 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.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-015-9437-y