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. 2024 Feb 23;21(3):4117-4141.
doi: 10.3934/mbe.2024182.

A stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps

Meng Gao  1 , Xiaohui Ai  1
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Free article

A stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps

Meng Gao et al. Math Biosci Eng. .
Free article

Abstract

By using the Ornstein-Uhlenbeck (OU) process to simulate random disturbances in the environment, and considering the influence of jump noise, a stochastic Gilpin-Ayala mutualism model driven by mean-reverting OU process with Lévy jumps was established, and the asymptotic behaviors of the stochastic Gilpin-Ayala mutualism model were studied. First, the existence of the global solution of the stochastic Gilpin-Ayala mutualism model is proved by the appropriate Lyapunov function. Second, the moment boundedness of the solution of the stochastic Gilpin-Ayala mutualism model is discussed. Third, the existence of the stationary distribution of the solution of the stochastic Gilpin-Ayala mutualism model is obtained. Finally, the extinction of the stochastic Gilpin-Ayala mutualism model is proved. The theoretical results were verified by numerical simulations.

Keywords: Ornstein-Uhlenbeck process; extinction; moment boundedness of solution; stochastic Gilpin-Ayala mutualism model; the existence of stationary distribution.

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