TY - JOUR
T1 - Stationary Distribution and Extinction of Stochastic Beddington-DeAngelis Predator-Prey Model with Distributed Delay
AU - Song , Mingyu
AU - Zuo , Wenjie
AU - Jiang , Daqing
AU - Hayat , Tasawar
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 187
EP - 204
PY - 2021
DA - 2021/04
SN - 2
DO - http://doi.org/10.12150/jnma.2020.187
UR - https://global-sci.org/intro/article_detail/jnma/18806.html
KW - Stochastic Beddington-DeAngelis predator-prey model, Distributed
delay, Stationary distribution, Extinction.
AB - <p style="text-align: justify;">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.</p>