Dynamic analysis of a stochastic regime-switching Lotka–Volterra competitive system with distributed delays and Ornstein–Uhlenbeck process

In this paper, we construct and analyze a stochastic regime-switching Lotka–Volterra competitive system with distributed delays and Ornstein–Uhlenbeck process. By the linear chain technique, we transform the stochastic model with weak kernel into an equivalent degenerate system. Firstly, we prove the existence and uniqueness of the global positive solution to the system. Then, we get the result of extinction and persistence in the mean of the x 1 and x 2 respectively. In addition, the sufficient conditions for the existence of the stationary distribution to the system are established by constructing some suitable Lyapunov functions. Finally, we provide some numerical examples to illustrate theoretical results, and some conclusions and analysis are given.