Asymptotic Behavior of a Stochastic Predator-Prey Model with Beddington-DeAngelis Functional Response and Lévy Jumps (Journal of Nonlinear Modeling and Analysis, 2024)
A stochastic two-prey-one-predator model with Beddington-DeAngelisfunctional response and Lévy jumps is proposed and investigated in this paper. First of all, we prove the existence and uniqueness of the global positivesolution, and stochastic ultimate boundedness of the solution. Next, undera 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 whitenoise nor Lévy noise is conducive to the persistence of the population. Finally,the theoretical results are verified by numerical simulations.
Keywords: Stochastic predator-prey model; Beddington-DeAngelis functional response; Lévy jump; Extinction; Persistence.