Asymptotic Behavior of a Stochastic Predator-Prey Model with Beddington-DeAngelis Functional Response and Lévy Jumps

Abstract

A stochastic two-prey-one-predator model with Beddington-DeAngelis functional response and Lévy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positive solution, and stochastic ultimate boundedness of the solution. Next, under a simple assumption, by using Itô formula and other important inequalities, some sufficient conditions are established to ensure the extinction and persistence in the mean of the system. The results show that neither strong white noise nor Lévy noise is conducive to the persistence of the population. Finally, the theoretical results are verified by numerical simulations.