Some new results on the dynamical behavior of non-autonomous logistic system with random perturbation

In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have similar dynamic behave with the deterministic system, but if the noise is sufficiently large, it will spoil these nice properties. Furthermore, we introduce a new research method for studying the stochastic equation and some new sufficient conditions for the stochastic bounded, stochastic permanence, extinction and global attractivity of the system are established. The corresponding results (see, for example, references [DQ Jiang, NZ Shi, and XY Li. Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation. J Math Anal Appl, 340:588-597, 2008; M Liu and K Wang. Persistence and extinction in stochastic non-autonomous logistic systems. J Math Anal Appl, 375:443-457, 2011; XY Li and XRMao. Population dynamical behavior of non-autonomous lotkavolterra competitive system with random perturbation. Discrete Contin Dyn Syst, 24:523-545, 2009]) are improved and extended.