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We study a stochastic logistic system with feedback control under regime switching. Sufficient conditions for extinction, non-persistence in the mean, weak persistence, and persistence in the mean are established. A very important fact is found in our results; that is, the feedback control is harmless to the permanence of species even under the regime switching and stochastic perturbation environments. Finally, some examples are introduced to illustrate the main results.

Permanence and Extinction of Stochastic Logistic System with Feedback Control under Regime Switching