Abstract
In this paper, a novel stochastic two-species competitive system with saturation effect is formulated, in which there exist two noise resources and their coupling mode is relatively complex and every noise source has effect on the intrinsic growth rates of both species. With the help of some suitable Lyapunov functions, sufficient conditions for stochastic permanence are established as exponential extinction, extinction, permanence in time average and asymptotic pathwise estimation of system. The effect of coupling noise on the asymptotic behaviors of the populations is shown.
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