Stationary distribution and global asymptotic stability of a three-species stochastic food-chain system

This paper intends to study some dynamical properties of a stochastic three-dimensional Lotka-Volterra system. Under some mild assumptions, we first introduce a simple method to show that the model has a global and positive solution almost surely. Secondly, we prove that this model has a stationary distribution. Then we study the global asymptotic stability of the positive solution. Finally, some numerical simulations are introduced to illustrate the theoretical results.