Abstract
This paper is concerned with a stochastic non-autonomous Gilpin-Ayala model. First, it is shown that this model has a global positive solution. Then sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence of the solution are established. The critical number between weak persistence and extinction is obtained. Finally, the lower- and upper-growth rate of the solution are investigated. Several numerical figures are introduced to illustrate the results. Some recent results are improved and generalized.
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