Limit Cyclic Bifurcation Of Two Differential Systems

In this paper, using the first order Melnikov function, we study the number of limit cycles of a class of piecewise quadratic differential systems with multiple parameters and a class of symmetrical Lienard systems. The first order Melnikov function, which is called the Abelian integral is one of the common tool.In chapter one, we introduce the background and main topics of our research. Also, we will describe the methods and main results obtained in this thesis.In chapter two, we introduce some basic definitions.In chapter three, we study on the number of limit cycles of a class of piecewise quadrat-ic differential systems with multiple parameters. It includes an isochronous center and an invariant line. By using the first order Melnikov function, we obtain 5 limit cycles, one more than [36].In chapter four, we presents a study on the number of limit cycles of a class of symmetrical Lienard systems. By using the method of stability-changing of a homoclinic loop, we can obtain 18 limit cycles,6 of which are alien limit cycles.