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

Authors: HONG QIU, WENMIN DENG

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

Keywords: Stochastic food-chain model, stationary distribution, global asymptotic stability,

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