Limit Cycles For Two Class Of Kukles Polynomial Differential Systems

In this paper, on the basis of the averaging method of bifurcation theory of dynamical systems, the maximum number of limit cycles of two classes of polynomial differential systems are studied. The full text of the content is divided into three chapters.The first chapter is the preface, in which we mainly describe the background and known results for the limit cycles of polynomial differential systems and bifurcation, and briefly illustrate the main works of the thesis.In the second chapter, we investigate the number of limit cycles for a class of gener-alized Kukles polynomial differential systems. We provide the number of limit cycles that the above differential systems can have bifurcating from the periodic orbits of a linear center using averaging method of first order, second order and third order.In the third chapter, the numbers of limit cycles for a class of generalized Kuk-les polynomial differential systems are studied. More precisely, by using the averaging method of first order, we obtain the number of limit cycle bifurcating from periodic orbits of nonlinear center.