Asymptotic stability of a stochastic Lotka–Volterra competition model with dispersion and Ornstein–Uhlenbeck process

To analyze the impacts of dispersion and environmental noise on population dynamics, in the current paper, we propose a stochastic Lotka–Volterra competition model in a patchy environment, where the fluctuations in the varying environment are characterized by an Ornstein–Uhlenbeck process. Besides that, we establish sufficient criteria for the asymptotic stability of the positive equilibrium of the system by adopting the Lyapunov function method.