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

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  • In this paper, we consider a non-autonomous stochastic Lotka-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 $B_i(t)$($i=1 ,\ 2,\cdots,\ n$) are independent standard Brownian motions. Some dynamical properties are discussed and the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.
    Mathematics Subject Classification: Primary: 62F10, 34F05; Secondary: 92B05.

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