Research On Dynamics Of Some Predator-prey Biological Models

The article research relevant properties of some prey-predator systems by using differential inequality theory, the generalized continuation theorem of coincidence degree theory and Lyapunov function method, such as the existence of positive periodic solution,the persistence and sufficient conditions of the positive almost periodic solutions, what’s more, it extend and develop some known results.This paper is composed of four chapters:In Chapter 1,introduces the historical development of biological mathematics, some research results on the subject by the predecessors, both here and abroad scholar do research of this subject and some related basic knowledge in this paper.In Chapter 2, globally asymptotic stability of positive periodic solution for predator-prey delay system with Holling-Ⅱ type functional response and harvesting is investigated. By using the continuation theorem of coincidence degree theory,we discuss the existence of positive periodic solutions of system; sufficient conditions for the globally asymptotic stability of the system are derived, and then give examples to illustrate the reliability of the conclusions.In Chapter 3,we consider a two-prey two-predator system. By using the differential Inequality theory and Lyapunov function, sufficient conditions for the persistence and the globally asymptotic stability of the system are derived. Through examples verify the correctness of the results at last.In Chapter 4, by using differential inequality theory and Lyapunov function method, the persistence of positive almost periodic solution, sufficient conditions for the globally asymptotic stability of the Holling-Ⅱ type functional response and pulse effect system are derived, then it extend and develop some known results.