Persistence and extinction of a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes

Advances in Difference Equations

article

Zhou, Dengxia¹  Liu, Meng²  Liu, Zhijun¹ 

[1] Department of Mathematics, Hubei Minzu University;School of Mathematical Science, Huaiyin Normal University

关键词: Persistence in the mean;    Extinction;    Itô’s formula;    Intensity of noise;   

DOI  :  10.1186/s13662-020-02642-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we use an Ornstein–Uhlenbeck process to describe the environmental stochasticity and propose a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes. For each species, sharp sufficient conditions for persistence in the mean and extinction are respectively obtained. The results demonstrate that the persistence and extinction of the species have close relationships with the environmental stochasticity. In addition, the theoretical results are numerically illustrated by some simulations.

【 授权许可】

CC BY