Two Classes Of Predator-Prey Model With Beddington-DeAngelis Functional Response And Delay In Patch Environment

In this dissertation,we mainly study two classes of predator-prey model with Beddington-DeAngelis functional response and delay.First,we introduced the relevant background and some preliminary knowledge.Then,we consider a predator-prey model with a single predator in the patch environment,by constructing a (1-function,using the auxiliary system and the comparison theorem,we obtained the sufficient conditions for permanence and extinction of this predator-prey model.Next,we consider a predator-prey model with two predators in the patch environment,considering the competitive relationship among the predator population.Using the comparison theorem,we obtained the sufficient conditions for permanence about the predator-prey model.Using the Poincar?e map we consider the existence about the positive periodic solution of this predator-prey model.Finally,by constructing an appropriate Lyapunov function,we prove that the system exists a unique positive solution of global asymptotic stability.