Existence And Global Asymptotic Stability Of Positive Periodic Solutions For Predator-prey System With Infinite Delay And Diffusion

In this paper, we study a periodic predator-prey system with Holling type III functional response, in which the prey species can diffuse among two patches but the predator is confined in one patch. By using the continuation theorem of coincidence degree theory and Liapunov functional, some sufficient conditions are obtained. And a non-autonomous stage-structured model of population growth in a polluted environment is considered.This paper is divided into three chapters. In the first chapter the authors give some preliminary including definitions and lemmas. In the next section existence of positive periodic solutions of system has been studied by using the continuation theorem of coincidence degree theorem proposed by Gaines and Mawhin;And by using the method of Lyapunov functional, the sufficient conditions of the global asymptotic stability of positive periodic solutions of the predator-prey model has been obtained. In the third chapter a non-autonomous stage-structured model of population growth in a polluted environment is considered and as a matter of fact, we have obtained the threshold of persistence and extinction for the asymptotically autonomous system.At the end of this paper, the author summarizes the innovations and proposes the direction of future work. Finally, related literatures are listed.