On a non-autonomous stochastic Lotka-Volterra competitive system

In this paper, we consider a general non-autonomous Lotka-Volterra competitive model with random perturbations. Sufficient conditions for stochastic permanence and extinction are established. Particularly, when these conditions are applied to a stochastic logistic equation, these conditions are sufficient and necessary. Some figures are also worked out to illustrate the main results. Some recent results are extended. Moreover, our results reveal that different types of stochastic noises have different effects on the permanence and extinction of the population.