Qualitative Analysis Of A Class Of Nonlinear Systems

This thesis focuses on the qualitative analysis of a class of nonlinear systems ofdi?erential equations, which contains the well-known Lie′nard systems as its specialcase.By using the qualitative theory and stability theory of ordinary di?erentialequations, we mainly study the boundedness and oscillation of solutions , the exis-tence and uniqueness of limit cycles , as well as the global asymptotic stability ofzero solution for such a class of the nonlinear systems.The paper is composed of five chapters.In chapter 1, we introduce the historical background and significance of prob-lems, the relevant preparatory knowledge and the major work of this paper.In chapter 2, we mainly discuss the boundedness and oscillation of solutionsof the system, given the necessary and su?cient conditions for the boundedness ofall solutions.At the same time, we also give several theorems about the oscillationof all solutions of the system.In chapter 3, by applying the traditional analytical methods of the qualitativetheory and the Poincare-Bendixson ring domain theorem, we give some theorem ofexistence of limit cycle of the system and relevant examples.Futhermore, we givethe non-existence theorem of limit cycle of the system.In chapter 4, by applying the method of uniqueness of the limit cycle of thegeneral Lie′nard systems, we obtain the uniqueness theorem of the limit cycle of thesystem.In chapter 5, by improving and promoting some typical results of Lie′nardequation, we obtain global asymptotic stability theorem of the system.