Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

In this paper, we consider a non-autonomous stochasticLotka-Volterra competitive system $ dx_i (t) = x_i(t)$[($b_i(t)$-$\sum_{j=1}^{n} a_{ij}(t)x_j(t))$$dt$$+\sigma_i(t) d B_i(t)]$, where $B_i(t)$($i=1 ,\ 2,\cdots,\ n$) areindependent standard Brownian motions. Some dynamical properties arediscussed and the sufficient conditions for the existence of globalpositive solutions, stochastic permanence, extinction as well asglobal attractivity are obtained. In addition, the limit of theaverage in time of the sample paths of solutions is estimated.