A stochastic Gilpin-Ayala nonautonomous competition model driven by mean-reverting OU process with finite Markov chain and Lévy jumps

• Published in: Electronic research archive Vol. 32; no. 3; pp. 1873 - 1900
• Main Authors: Gao, Meng, Ai, Xiaohui
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: extinction; moment boundedness of solution; ornstein-uhlenbeck (ou) process; stochastic gilpin-ayala nonautonomous competition model; the existence of stationary distribution
• ISSN: 2688-1594; 2688-1594
• DOI: 10.3934/era.2024086

The Ornstein-Uhlenbeck (OU) process was used to simulate random perturbations in the environment. Considering the influence of telegraph noise and jump noise, a stochastic Gilpin-Ayala nonautonomous competition model driven by the mean-reverting OU process with finite Markov chain and Lévy jumps was established, and the asymptotic behaviors of the stochastic Gilpin-Ayala nonautonomous competition model were studied. First, the existence of the global solution of the stochastic Gilpin-Ayala nonautonomous competition model was proven by the appropriate Lyapunov function. Second, the moment boundedness of the solution of the stochastic Gilpin-Ayala nonautonomous competition model was discussed. Third, the existence of the stationary distribution of the solution of the stochastic Gilpin-Ayala nonautonomous competition model was obtained. Finally, the extinction of the stochastic Gilpin-Ayala nonautonomous competition model was proved. The theoretical results were verified by numerical simulations.