Analysis of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes

Dongsheng Xu, Ming Liu and Xiaofeng Xu

Physica A: Statistical Mechanics and its Applications, 2020, vol. 537, issue C

Abstract: In this paper, we investigate the dynamics of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes. We first show the existence and uniqueness of the global positive solution to the system with positive initial values. In some case, the stochastic boundedness and stochastic permanence are obtained. Then, under some conditions, we prove the persistence in mean and extinction of the stochastic system. Moreover, under certain parametric restrictions, we obtain that the system has a stationary distribution which is ergodic. Finally, some numerical simulations are carried out to support our results.

Keywords: Stochastic predator–prey system; Leslie–Gower; Holling-type IV; Persistence and extinction; Stationary distribution and ergodicity (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315699

DOI: 10.1016/j.physa.2019.122761

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