The Study Of Periodic Solutions And Stability On Some Mathematical Ecology Models

There are three chapters in this thesis.The first chapter is overview, in which we introduce the developing status about predator-prey system of Mathematical Ecology and some related works that we have done.In the second chapter, we discuss two kinds of non-autonomous predator-prey system governed by difference equations. For the former, we consider the discrete time predator-prey system with Holling II type functional response, by using the method of coincidence degree and its related continuation theorem and the method of Lyapunov function, we obtain some sufficient conditions about the existence and global asymptotic stability of positive periodic solutions. For the latter, we consider a delayed discrete time three species with Beddington-DeAngelis functional response food chain model, using the similar method, we obtain the sufficient conditions on the existence of positive periodic solutions, which extends Huo Haifeng and Li Wantong's results in .In the third chapter, we study the limit cycles of two kinds of predator-prey system with constant-rate stocking, and give the sufficient conditions for existence and nonexistence of limit cycles.