Periodic Orbits Analysis in a Class of Planar Liénard Systems with State-Triggered Jumps

Abstract

In this paper, we investigate the existence problem of periodic orbits for a planar Liénard system, whose solution mappings are interrupted by abrupt changes of state. We first present the geometrical properties of solutions for the planar Liénard system with state impulses, then by using Bendixson theorem of impulsive differential equations and successor function method, several new criteria on the closed orbits and discontinuous periodic orbits are established in the impulsive Liénard system.