Stochastic mutualism model under regime switching with Lévy jumps

Hongjun Gao and Ying Wang

Physica A: Statistical Mechanics and its Applications, 2019, vol. 515, issue C, 355-375

Abstract: This paper is concerned with a stochastic mutualism model under regime switching with Lévy jumps. To begin with, the existence and uniqueness of the global positive solution is proved with any given positive initial value. Then, the sufficient conditions for stochastic permanence are established. The critical value between extinction and persistence in mean is also obtained. In addition, under some suitable conditions, we proved that there is a unique stationary distribution for the system without Lévy jumps. Our method relies on the Lyapunov function analysis and the Fredholm alternative. The results demonstrate that regime switching may contribute to the permanence but jump noise may suppress the permanence.

Keywords: Mutualism model; Stochastically permanence; Extinction; Ergodicity (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:515:y:2019:i:c:p:355-375

DOI: 10.1016/j.physa.2018.09.189

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