Dynamical behavior of a stochastic two-species Lotka-Volterra
competition system in a patchy environment
AbstractIn 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.