The Maximum Number Of Limit Cycles Of Two Polynomial Systems

As an introduction, in the first chapter we introduce the background of our research and main topics that we will study in the following chapters. We also give a description of our methods and results detained in this thesis in the first chapter.In the second chapter, we give some basic definitions and also introduce some known results as lemmas. We give a general theorem on Hopf bifurcation of limit cycles, which plays a very important role in studying the maximum number of limit cycles.In the third chapter, we study the number of limit cycles of a polynomial near-Hamiltonian system. We get some coefficients by using an expansion of Melnikov func-tion near the center. By using a general theorem on Hopf bifurcation of limit cycles, a lower bound for the maximum number of isolated zeroes of the corresponding Abelian integral is gived, which give a lower bound for the maximum number of limit cycles.In the fourth chapter, we study the number of limit cycles of a polynomial Lienard systems x=y-(?), y=-χ(1+χ). By using a general theorem on Hopf bifurcation of limit cycles, we give some concrete Hopf cyclicity.