Persistence and extinction of an impulsive stochastic logistic model with infinite delay

Abstract

This paper considers an impulsive stochastic logistic model with infinite delay at the phase space $C_{g}$. Firstly, the definition of solution to an impulsive stochastic functional differential equation with infinite delay is established. Based on this definition, we show that our model has a unique global positive solution. Then we establish the sufficient conditions for extinction, nonpersistence in the mean, weak persistence and stochastic permanence of the solution. The threshold between weak persistence and extinction is obtained. In addition, the effects of impulsive perturbation and delay on persistence and extinction are discussed, respectively. Finally, numerical simulations are introduced to support the theoretical analysis results.