The Qualitative Analysis Of A Class Of Predator-Prey Model With Sublinear Functional Response Function

In this thesis, using the qualitative theory and stability theory of ordinary differential equation, we study the global stability of equilibrium, existence and uniqueness of limit cycle for a predator-prey model with sublinear functional response function.This paper is composed of five chapters.In the first chapter, we introduce the background of problems which will be investigated and the main results of this paper. At the same time, some basic theory of the qualitative theory and stability theory of ordinary differential equation are given.In chapter 2, we discuss the global stability of positive equilibrium, existence of limit cycle for a general predator-prey model with functional response function. The theoretical analysis are verified by numerical simulations.Chapter 3 mainly considers a class of predator-prey model with sublinear functional response function. We deduce some sufficient conditions ensuring stability of equilibrium, nonexistence , existence as well as uniqueness of the limit cycle around the positive equilibrium.The purpose of chapter 4 is to study a predator-prey model with sublinear functional response function and sublinear density control function. Some results dealing with stability of equilibrium, nonexistence , existence as well as uniqueness of the limit cycle around the positive equilibrium of the model are obtained. Our results extend some previous work of others researchers.In the last chapter, we consider a predator-prey model with sublinear functional response function, sublinear density control function and constant stocking rate. The properties of equilibrium, existence and uniqueness of the limit cycle around the positive equilibrium investigated. Our results prove and extend some existing results.