Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation

In this paper, we develop a new stochastic mutualism population model dxi(t)=xi(t)[(ri+n∑j=1aijxj(t))dt+σiσxi(t)dBi(t)],i=1,2,...,n. By constructing suitable Lyapunov functions, we show the system has a stationary distribution. We also discuss the pathwise behaviour of the solution. The conclusions of this paper is very powerful since they are independent both of the system parameters and of the initial value. It is also independent of the noise intensity as long as the noise intensity σ^2 i 0 . Computer simulations are used to illustrated our results.