The Research On Some Predator-Prey Models With Beddington-DeAngelis Functional Response

The predator-prey system is a very important part in ecology, and the mathematical method has been well applied in the research. Recently, because of its widely applications, the predator-prey system has received a great deal of attention of mathematicians and biologists. This thesis mainly studies the dynamics of three classes of predator-prey systems with Beddington-DeAgelis functional response. A series of results are obtained, which of them improve or extend the results in the literations.In this paper we first introduce the background and the recent works of the predator- prey system. In the second chapter, we consider the permanence property of a classes of delayed Beddington-DeAgelis type predator-prey system, we obtain some sufficient conditions ensuring the permanence of the system by means of in-equation method, and we also give the conditions in which the system will go to perdition. In the third chapter, we consider a class of Beddington-DeAgelis type predator-prey system with distribute time delays, we obtain some conditions ensuring the existence of the periodic solutions by means of coincidence degree theorem, which has extend the results in the literations. In the fourth chapter, we focus on the permanence of the Beddington-DeAgelis type predator-prey system with stage structure. Using Liapunov functional method, we obtain some conditions ensuring the permanence of the system. In the end, we discuss the equilibrium's global asymptotic stability of this system.