Stationary Distribution and Extinction of Stochastic Beddington-DeAngelis Predator-Prey Model with Distributed Delay (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we consider the dynamics of the stochastic Beddington-DeAngelis predator-prey model with distributed delay. First, we adopt thelinear chain technique to transfer the stochastic system with strong kernelinto an equivalent degenerated stochastic system made up four equations.Then we give the existence and uniqueness of the global positive solution.Next, sufficient conditions for persistence and extinction of two species are obtained. Particularly, the existence of the stationary distribution is establishedby constructing a suitable Lyapunov function. Finally, numerical simulationsillustrate our theoretical results. It shows that the system still maintains thestability for the smaller white noises, but the stronger white noises will leadto the extinction of one or two species.
Keywords: Stochastic Beddington-DeAngelis predator-prey model; Distributed delay; Stationary distribution; Extinction.