Stability of stochastic Gilpin-Ayala model driven by α-stable process under regime switching

Xuekang Zhang, Huisheng Shu and Dajun Liu

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 10, 3459-3471

Abstract: In this paper, stochastic Gilpin-Ayala model driven by α-stable process under regime switching is presented. Firstly, we prove the existence and uniqueness of the solution for the stochastic model. Then, under certain conditions, the almost sure exponential stability and pth moment exponential stability of the trivial solution are obtained. The results indicated that the α-stable noises can make the trivial solution stable under some conditions. Computer simulations are presented to illustrate our theory.

Date: 2024
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DOI: 10.1080/03610926.2022.2154611

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