Dynamical analysis of a stochastic three-species predator–prey system with distributed delays

A stochastic two-prey one-predator system with distributed delays is proposed in this paper. Firstly, applying the linear chain technique, we transform the predator–prey system with distributed delays to an equivalent system with no delays. Then, by use of the comparison method and the inequality technique, we investigate the stability in mean and extinction of species. Further, by constructing some suitable functionals, using M-matrix theory and three important lemmas, we establish sufficient conditions assuring the existence of distribution and the attractivity of solutions. Finally, some numerical simulations are given to illustrate the main results.