Analysis of a stochastic Leslie-Gower predator-prey system with Beddington-DeAngelis and Ornstein–Uhlenbeck process

Yifan Wu; Xiaohui Ai; Yifan Wu; Xiaohui Ai

doi:10.3934/era.2024018

Electronic Research Archive

2024, Volume 32, Issue 1: 370-385. doi: 10.3934/era.2024018

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Theory article

Analysis of a stochastic Leslie-Gower predator-prey system with Beddington-DeAngelis and Ornstein–Uhlenbeck process

Yifan Wu ,
Xiaohui Ai ^,

School of Science, Northeast Forestry University, China

Received: 05 October 2023 Revised: 03 December 2023 Accepted: 18 December 2023 Published: 27 December 2023

In this paper, a stochastic Leslie-Gower model with Beddington-DeAngelis functional response driven by the Ornstein-Uhlenbeck process is studied. Some asymptotic properties of the solution of the stochastic Leslie-Gower model are introduced: the existence and uniqueness of the global solution of the model are demonstrated, the ultimate boundedness of the model is analyzed, the existence of the stationary distribution of the model is proven, and the conditions for system extinction are discussed. Finally, numerical simulations are utilized to verify our conclusions.
- Leslie-Gower,
- Beddington-DeAngelis,
- Ornstein-Uhlenbeck,
- stationary distribution,
- extinction
Citation: Yifan Wu, Xiaohui Ai. Analysis of a stochastic Leslie-Gower predator-prey system with Beddington-DeAngelis and Ornstein–Uhlenbeck process[J]. Electronic Research Archive, 2024, 32(1): 370-385. doi: 10.3934/era.2024018

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Abstract

In this paper, a stochastic Leslie-Gower model with Beddington-DeAngelis functional response driven by the Ornstein-Uhlenbeck process is studied. Some asymptotic properties of the solution of the stochastic Leslie-Gower model are introduced: the existence and uniqueness of the global solution of the model are demonstrated, the ultimate boundedness of the model is analyzed, the existence of the stationary distribution of the model is proven, and the conditions for system extinction are discussed. Finally, numerical simulations are utilized to verify our conclusions.

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