Persistence and Nonpersistence of a Food Chain Model with Stochastic Perturbation

Abstract

We analyze a three species predator-prey chain model with stochastic perturbation. First, we show that this system has a unique positive solution and its $p$th moment is bounded. Then, we deduce 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.