Stability Analysis Of Three-species Predator-prey System With Beddington-DeAngelis Functional Response

In this paper, we mainly study the stability behavior of three-species non-autonomous predator-prey system with time delay and Beddington-DeAngelis functional response. By analyzing the three models in the paper, we mainly obtain the sufficient conditions for permanence of the system and global stability of positive periodic solution, and present numerical simulation to validate the conclusions.In chapter one, we mainly introduce the background, current situation, some cor-responding main definitions and theorems about predator-prey model with Beddington-DeAngelis functional response.In chapter two, we mainly study the permanence and periodic solution of a predator-prey model with Beddington-DeAngelis functional response consisting of two competitive prey population and a stage structure on predator. In the chapter, we can obtain the suffi-cient conditions for permanence of the model, extinction, existence and global stability of positive periodic solution through comparative principle, Brouwer theorem and a Liapunov function.In chapter three, we mainly study the periodic solution of three-species clockwise chain predator-prey model with Beddington-DeAngelis functional response and nonlinear diffusion on prey. In the part, we can get the sufficient conditions for existence and global stability of positive periodic solution through continuation theorem of coincidence degree theory and a Liapunov function.In chapter four, we mainly study the permanence and periodic solution of a predator-prey model with Beddington-DeAngelis functional response consisting of prey refuges and a stage structure on predator. In the part, we can obtain the sufficient conditions for per-manence of the model, existence and global stability of positive periodic solution through comparative principle, Brouwer theorem and a Liapunov function.