Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.

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We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.

This paper studies two widely used stochastic non-autonomous logistic models. For the first system, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The critical number between weak persistence and extinction is obtained. For the second system, sufficient criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and stochastic permanence are established. The critical number between weak persistence in the mean and extinction is obtained. It should be pointed out that this research is systematical and complete. In fact, the behaviors of the two models in every coefficient cases are cleared up by the results obtained in this paper.