Global Dynamics of a Stochastic Two-Prey One-Predator Model with <i>S</i>-Type Distributed Delays and Lévy Noises

Abstract

In this paper, a stochastic two-prey one-predator model with S-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito's formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat's conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.