Dynamics of non-autonomous stochastic Gilpin–Ayala competition model with time-varying delays

In this paper the non-autonomous stochastic Gilpin–Ayala competition model with time-dependent delay is considered. We prove existence and uniqueness of the global positive solution and various properties of that solution such as boundedness, moment and pathwise estimation, extinction, non-persistence in time average and weak persistence. In addition, we give a special case of the considered system and impose its properties. All studied features are natural requirements from the biological point of view. Furthermore, examples with numerical simulations are given to illustrate our results.