The Qualitative Analysis Of The Liénard System

In this paper, we discuss a kind of equations, that is the properties of a local or global center for a Liénard system. This paper divides into five chapters:In chapter one, we review briefly the history and development situations of differential equations, and give the introduces of the paper.In chapter two, first, we introduce the concepts and theories of dynamics and critical point, finally, we introduce concepts and defines and theories of the Liénard system.In chapter three, we discuss the conditions of a local or global center for the Liénard system. By using comparison theorem and linear approximation, we give some sufficient conditions to guarantee the origin is a local or global center. Therefore, some results of Refs.[1,2 are generalized.In chapter four, the connections among the attractor, the attractor neighborhood and the domain of influence are investigated. A necessary and sufficient condition of the existence of the quasi-attractor is established.In chapter five, we give the briefly conclusion of this paper and propose the problem for further studies.