Persistence and non-persistence of a stochastic food chain model with finite delay

In this paper, we study a three species predator-prey time-delay chain model with stochastic perturbation. First, we analyze that this system has a unique positive solution. Then, we deduce the conditions that the system is persistent in time average. After that, conditions for the system going to be extinction in probability are established. At last, numerical simulations are carried out to support our results.