On a three-species stochastic hybrid Lotka-Volterra system with distributed delay and Levy noise

Abstract

In this paper, a three-species stochastic hybrid Lotka-Volterra system with distributed delay and Levy noise is proposed and studied by using stochastic analytical techniques. First, the existence and uniqueness of global positive solution with positive initial condition is proved. Then, sufficient conditions for persistence in mean and extinction of each species are established. Finally, some numerical simulations are provided to support our results.