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.