Dynamics of an Impulsive Stochastic Predator–Prey System with the Beddington–DeAngelis Functional Response

Taking impulsive effects into account, an stochastic predator–prey system with the Beddington–DeAngelis functional response is proposed in this paper. First, transformed equivalent without pulses. Then, by constructing suitable functionals and applying extreme-value theory of quadratic functions, sufficient conditions on existence periodic Markovian processes are provided. The uniform continuity global attractivity solutions also investigated. Additionally, we investigate extinction permanence mean all species help comparison methods inequality techniques. Sufficient ergodicity stationary distribution for autonomous non-impulsive case given. Finally, numerical simulations performed to illustrate main results.