The Number Of Limit Cycles Of A Class Of Plane Piecewise Smooth Nearly Integrable System

The researches on piecewise smooth(PWS)dynamical systems has recently shown that the bifurcation methods for finding limit cycles have been popularized from smooth systems to non-smooth systems.The methods such as the averaging method,Melnikov function and so on,are extended to be applied to planar non-smooth systems.In this paper,we mainly focus on a class of planar piecewise smooth integrable systems.The maximal number of limit cycles in Hopf bifurcation has been obtained by the first order Melnikov function.This paper is organized as follows.The first chapter introduces the source of the research topic,research status,research methods and main conclusions of this paper.After reviewing some basic knowledge,the second chapter simultaneously introduces some definitions and formulas related to this paper.In the third chapter,the expansion of Melnikov function at h=0 has been derived.Then we obtain the maximal number of limit cycles in Hopf bifurcation of the system in this paper.