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Boundedness, persistence and extinction of a stochastic non-autonomous logistic system with time delays. (English) Zbl 1252.60058
Summary: We investigate the stochastic non-autonomous logistic system with time delays. Under two simple assumptions on the environmental noise, it is shown that the stochastic system has a unique global positive solution, and this positive solution is asymptotically bounded. The conditions for extinction, weak persistence of solutions are also obtained by the exponential martingale inequality. Finally, a numerical example is provided to illustrate our results.
60H10Stochastic ordinary differential equations
34K50Stochastic functional-differential equations
34K25Asymptotic theory of functional-differential equations
92D25Population dynamics (general)
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