Stationary distribution of a stochastic vegetation–water system with reaction–diffusion

Considering the impact of the mean-reverting Ornstein–Uhlenbeck (O–U) process in an ecosystem, the stable distribution of a stochastic reaction–diffusion vegetation–water system was studied. We proved the existence and uniqueness of the global positive solution of the system by constructing the Lyapunov function. We established the existence and uniqueness of the stable distribution of the solution of the system.