Stationary Distribution and Extinction of Stochastic Beddington-DeAngelis Predator-Prey Model with Distributed Delay

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.

Author Details

Mingyu Song

Wenjie Zuo

Daqing Jiang

Tasawar Hayat