The Research On Persistence And Periodic Solutions Of Some Classes Of Holling Type Predator-Prey Systems

In recent years, the predator-prey relation has become a very important part in mathematics and ecology. The predator-prey theory has a great value in both theory and application. One of the most important questions in population ecology is to find the permanence conditions for the species, which has received a great deal of attention of many mathematicians and biologists. Based on the existed Lotka-Volterra population models, we consider some classes of predator-prey systems with Holling functional response. We make much investigation in the existence of periodic solutions and the permanence of these new models. This thesis is composed of four chapters.In the first chapter, we introduce the history of mathematical ecology's development, the existed related work and the origin of the problems we discussed. The main work of this paper is also simply introduced in this chapter. In the second chapter, we consider a three-species ratio-dependent predator-prey system with discrete time and Holling II type functional response. By using the continuation theorem of topology degree theory, we obtain suficient conditions for the existence of positive periodic solutions of this system. Obtained results are same as the known results of the corresponding differential system. The purpose of the third chapter is to study the permanence of a nonautonomous two species Holling III type predator-prey system with delays. We obtain some sufficient conditions ensuring the permanence of the system by means of inequality and analyse. Finally, in the fourth chapter, we consider two stage-structured ratio-dependent predator-prey systems with Holling III type functional response. By constructing a Liapunov function, we obtain some sufficient conditions which ensure the persistence of the first system, and the existence of periodic solutions of the second system which is established by using coincidence degree theory.