Bifurcation of limit cycles near a heteroclinic loop with nilpotent cusps

Abstract

In this paper, we study the relation between the coefficients in the expansions of two Melnikov functions near a heteroclinic loop with nilpotent cusps. Based on this relation, we give a condition of obtaining limit cycles near the heteroclinic loop. Further, we present a method to compute more coefficients in the expansions of two Melnikov functions near the heteroclinic loop. As an application, we consider a class of Liénard systems and study the number of limit cycles bifurcated from a heteroclinic loop and an elementary center.