Stationary Distribution and Extinction of Stochastic Beddington-DeAngelis Predator-Prey Model with Distributed Delay
Year: 2020
Author: Mingyu Song, Wenjie Zuo, Daqing Jiang, Tasawar Hayat
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 187–204
Abstract
In this paper, we consider the dynamics of the stochastic Beddington-DeAngelis predator-prey model with distributed delay. First, we adopt the linear chain technique to transfer the stochastic system with strong kernel into 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 established by constructing a suitable Lyapunov function. Finally, numerical simulations illustrate our theoretical results. It shows that the system still maintains the stability for the smaller white noises, but the stronger white noises will lead to the extinction of one or two species.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2020.187
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 2 : pp. 187–204
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Stochastic Beddington-DeAngelis predator-prey model Distributed delay Stationary distribution Extinction.