Long-time Behavior Of A Stochastic Mutualism System

In this paper, we study the stochastic mutualism model of two populations below,We consider the system of two species is in the same environment. We assume that their white noise is the same. Thus our research system is degraded. Under the condition of a11a22>a12a21, C1= r1-σ2/2> 0, c2= r2-ρ2/2> 0, we use the theory of Markov semi-group to study the property of asymptotic stability for the stochastic process (X(t), Y(t)), and we get the density of the distributions of (X(t),Y(t)) exists an invariant density.