Persistence and extinction of an n-species mutualism model with random perturbations in a polluted environment

An n-species stochastic Lotka-Volterra cooperative model in a polluted environment is proposed and studied. For each species, sufficient conditions for extinction, non-persistence in the mean and weak persistence in the mean are established. The threshold between weak persistence in the mean and extinction is obtained. Several numerical figures are also worked out to validate the theoretical results.