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

Abstract

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.

Keywords

• stochastic gilpin-ayala nonautonomous competition model
• moment boundedness of solution
• ornstein-uhlenbeck (ou) process
• the existence of stationary distribution
• extinction