Extinction and strong persistence in the Beddington–DeAngelis predator–prey random model

This paper studies a predator–prey model with a Beddington–DeAngelis type functional response under the stationary Ornstein–Uhlenback process. First, we prove the existence and uniqueness of the global positive solution for the given system for any initial datum. Second, we turn to its internal structures and establish the existence of a compact forward‐absorbing set as well as a forward attracting one. Finally, we carry out some numerical simulations to support the theoretical results.