Asymptotic behavior of a stochastic Gilpin–Ayala predator–prey system with time-dependent delay

A 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.