@article{Gao2024, 
author = {Meng Gao and Xiaohui Ai},
title = {A stochastic Gilpin-Ayala nonautonomous competition model driven by mean-reverting OU process with finite Markov chain and Lévy jumps},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {3},
pages = {1873-1900},
keywords = {stochastic Gilpin-Ayala nonautonomous competition model, moment boundedness of solution, Ornstein-Uhlenbeck (OU) process, the existence of stationary distribution, extinction},
url = {https://www.sciopen.com/article/10.3934/era.2024086},
doi = {10.3934/era.2024086},
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.}
}