Abstract
Two stochastic single-species models are considered in this paper. For the first model, we discuss the existence and uniqueness of the solution, recurrence and the existence of stationary distribution. And the threshold analysis of strong stochastic persistence and extinction is obtained. For the second model, we explore the existence and uniqueness of the solution. In addition, we study the stability for the model and the existence of stationary distribution. Finally the numerical simulations are carried out to support our results for the two models.
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