Class Of Differential Autonomous System Of Qualitative Analysis

This thesis is devoted to qualitative analysis for some planar polynomial differential autonomous systems. It is composed of four chapters.In Chapter 1, the background and present conditions are introduced and summarized of the existence and uniqueness of limit cycles for planar polynomial differential autonomous systems.In Chapter 2, by means of qualitative analysis, this thesis solves the existence and uniqueness of limit cycles for a cubic Kolmogorov system.In Chapter 3, this thesis changes a class of higher polynomial system into a Lienard system by transformation. Applying Hopf bifurcation theorm and uniqueness theorm by Zhang Zhifen, this thesis proves the existence and uniqueness of limit cycle for the system.In Chapter 4, a class of biochemistry reaction model is discussed by the method qualitative analysis. In the end, by turning it into a Lienard system, the existence and uniqueness of limit cycle are proved.