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a b s t r a c tA stochastic Gilpin-Ayala predator-prey model with time-dependent delay is studied in this paper. We establish sufficient conditions for the existence of a global positive solution of the considered system. Then, we prove stochastically ultimate boundededness and obtain certain asymptotic results regarding the long-time behavior of trajectories of the solution. Also, sufficient criteria for extinction of species for a special case of the considered system are given. At the end, numerical simulations are carried out to support our results.

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In this paper we study the Gilpin-Ayala competition system with random perturbation which is more general and more realistic than the classical LotkaVolterra competition model. We verify that the positive solution of the system does not explode in a finite time. Furthermore, it is stochastically ultimately bounded and continuous a.s. We also obtain certain results about asymptotic behavior of the stochastic Gilpin-Ayala competition model.

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