Boundedness, persistence and extinction of a stochastic non-autonomous logistic system with time delays

This paper investigates 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.