On the Number of Limit Cycles Bifurcating from a Compound Polycycle

Abstract

This paper focuses on the number of limit cycles bifurcating from a symmetrical compound polycycle with three saddles. We use two methods, the Melnikov function method and the method of stability-changing of a homoclinic loop or a double homoclinic loop to study this problem. We find 15 limit cycles and 16 limit cycles respectively with four alien limit cycles under certain conditions.