Existence of homoclinic orbit in generalized Liénard type system

Abstract

The object of this paper is to study the existence and nonexistence of an important orbit in a generalized Liénard type system. This trajectory is doubly asymptotic to an equilibrium solution, i.e., an orbit which lies in the intersection of the stable and unstable manifolds of a critical point. Such an orbit is called a homoclinic orbit.

Keywords

• liénard system
• homoclinic orbit
• planar system
• dynamical systems