Limit Cycles For Some Three-dimensional Polynomial Differential Systems Near The Z-axis

In the first chapter, We introduce the background of our research and main topicsthat we will study in the following chapters. We also give a description of our methodsand results.In the second chapter, We introduce averaging method and its application in thetwo-dimensional polynomial di?erential systems. In this chapter, we use this methodto prove the limit cycles for a class of linear perturbed system. moreover, this methodprovide convenience for ?nding the limit cycles and their stability for some polynomialdi?erential system.In the third chapter, we study the limit cycles for a class of three-dimensionalpolynomial differential systems near the z-axis. For the purpose, we also assume certaincondition, besides using averaging method, then obtain the number of matching limitcycles. In the end, We take a example to illustrate the existence of maximum numberof limit cycles.In the fourth chapter, we study the limit cycles for another class of three-dimensionalpolynomial differential systems near the z-axis. We use the method in chapter 2 and3, and apply some very flexible skill, then obtain the number of corresponding limitcycles. At last, we also take some examples to show the correctness of above conclusion.