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

Abstract This paper considers an impulsive stochastic logistic mode l with infinite delay at the phase space Cg. Firstly, the definition of solution to an impulsive stochas tic functional differential equation with infinite delay is establi shed. 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 th e mean, weak persistence and stochastic permanence of the solution. The threshold betwe en weak persistence and extinction is obtained. In addition, the effects of impulsi ve perturbation and delay on persistence and extinction are discussed, respectively. F inally, numerical simulations are introduced to support the theoretical analysis results .