Bifurcation of Limit Cycles in Small Perturbation of a Class of Lienard Systems

Abstract

In this article, we study the limit cycle bifurcation of a Lienard system of type (5, 4) with a heteroclinic loop passing through a hyperbolic saddle and a nilpotent saddle. We study the least upper bound of the number of limit cycles bifurcated from the periodic annulus inside the heteroclinic loop by a new algebraic criterion. We also prove at least three limit cycles will bifurcate and six kinds of different distributions of these limit cycles are given. The methods we use and the results we obtain are new.