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

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 stabi...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2024-05, Vol.53 (10), p.3459-3471
Main Authors: Zhang, Xuekang, Shu, Huisheng, Liu, Dajun
Format: Article
Language:English
Subjects:
almost sure exponential stability
pth moment exponential stability
regime switching
Stability
Stochastic Gilpin-Ayala model
Stochastic models
Switching
α-stable process
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Summary: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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2022.2154611