Abstract

In this paper, we propose and analyze a higher-order stochastically perturbed two-species Lotka-Volterra competition system in a patchy environment. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by constructing a series of suitable Lyapunov functions. Moreover, we also obtain the asymptotic behavior of the solutions around the boundary equilibrium of the deterministic system.