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

• Published in: Journal 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
• Language: English
• 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

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...