On the Uniqueness of Limit Cycles in Codimension Two Bifurcations

Abstract

In this paper we present a survey on the uniqueness of limit cycles bifurcating from a center, homoclinic loop or a heterclinic loop in planar systems, introducing five bifurcation theorems, and then apply the theorems to the study of codimension two bifurcations, obtaining a complete analysis on the uniqueness of limit cycles.