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

摘要

A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in 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.