On Hopf Bifurcation By Perturbing Non-smooth Quadratic Reversible Systems

Recently,many researchers have paid much attention to the piecewise smooth differential systems.Some bifurcation methods for finding limit cycles have been developed from smooth systems to piecewise smooth systems.In this paper,we consider the nongeneric quadratic reversible system with piecewise polynomial perturbations.We use the expansions of the first order Melnikov function to investigate the maximal number of limit cycles in Hopf bifurcation for the perturbed system.The paper is organized as follows.In Chapter 1,we introduce the historical background and current situation of the research.Also,we introduce the main results of this paper.In Chapter 2,we introduce some methods of studying the Hopf bifurcation for piecewise smooth systems.Then,we analyze the algebraic structure of the Melnikov function of the system in this paper and obtain the expansion of the Melnikov function at the center.In Chapter 3,we prove the main results.