Dynamics Of Discrete Predator-prey System With Beddington-DeAngelis Functional Response

In population dynamics,predator-prey system with functional response have grasped the eyeballs of many science investigators.Recently,some continuous dynamic models with Beddington-DeAngelis functional response have discussed.The discrete models governed by difference equations are more appropriate than the continuous ones governed by differential equations when the size of the population is rarely small or the population has non-overlapping generations.Therefore, it is interesting and important to further study the mathematical model of predator-prey system with Beddington-DeAngelis functional response.In this paper,we systematically study the dynamics of discrete predator-prey system with Beddington-DeAngelis functional response. It may be briefly summed up as follows:In the first place,the new conditions which guarantee the permanence of the discrete predator-prey system with Beddington-DeAngelis functional response is obtained by comparison principle and some skills of inequalities. Moreover, By using the Brouwer fix point theory,the sufficient conditions ensuring the existence of positive periodic solutions of the discrete predator-prey system with functional response are obtained. The result partly improve and extend some recent works.In the second place, we systematically study the stability of discrete predator-prey system with Beddington-DeAngelis functional response.In this section,we primarily introduce some elementary knowledge and findings about the stability of discrete system.Then,some sufficient conditions are obtained which guarantee the global asymptotic stability of this discrete system by permanence and constructing suitable Lyapunov function.