Ergodic stationary distribution and extinction of a n-species Gilpin–Ayala competition system with nonlinear random perturbations

Abstract Considering the complexity of random variations in ecosystem, a n-species Gilpin-Ayala competition system with nonlinear noises is studied in this paper. Using our developed ϵ -stochastic criterion method in eliminating nonlinear perturbations, we construct several suitable Lyapunov functions to obtain the threshold for the existence and uniqueness of an ergodic stationary distribution, which reflects population coexistence in a long term. Moreover, we establish the sufficient conditions for population extinction. Finally, several numerical simulations are performed and our analytical results are discussed by comparison with the existing papers.