STATIONARY DISTRIBUTION OF A LOTKA-VOLTERRA MODEL WITH STOCHASTIC PERTURBATIONS AND DISTRIBUTED DELAY

This paper devotes to the existence of a stationary distribution for a one-prey and two-predator Lotka-Volterra model with stochastic nonlinear perturbations and distributed delay. The studied autonomous system is first proved having a unique global and positive solution. Then, through construct-ing appropriate Lyapunov function and using Itô formula, sufficient conditions guaranteeing the existence of a stationary distribution of the stochastic system are obtained. Some numerical simulations are also provided in the end to illustrate the main results.