The Long Time Behavior of a Stochastic Logistic Model with Infinite Delay and Impulsive Perturbation

Abstract

This paper considers a stochastic logistic model with infinite delay and impulsive perturbation. Firstly, with the space $C_{g}$ as phase space, the definition of solution to a stochastic functional differential equation with infinite delay and impulsive perturbation is established. According to this definition, we show that our model has an unique global positive solution. Then we establish the sufficient and necessary conditions for extinction and stochastic permanence of the model. In addition, the effects of impulsive perturbation and delay on extinction and stochastic permanence are discussed, respectively.