Types Of Differential Autonomous System Limit Cycle Existence And Uniqueness

The thesis is devoted to studying center-focus determination and existence and uniqueness of limit cycles for some planar polynomial differential systems. It consists of four chapter.In Chapter l,the background and present conditions are introduced and summarized for the study of center-focus determination and existence and uniqueness of limit cycles for planar polynomial systems.In Chapter 2, the nonexistence of limit cycles and global phase po -rtraits for a class of quadratic system is studied. At the same time, a class of dynamical system in biochemistry reaction is discussed by using the method of qualitative analysis. In addition, the existence,nonexistence and uniqueness of a limit cycle are proved.In Chapter 3, A class of cubic system is investigated and the first 7 values of singular point are computed accurately. and the integrability conditions are also obtained.In Chapter 4, A class of n+1 kolmogorov system is studied by using the method of qualitative analysis. The stability of equilibrium, the existence of the limit cycle are discussed under the condition of a₄ > 0 and a₄ < 0.