Dynamics of the Predator-Prey Model with Beddington-DeAngelis Functional Response Perturbed by Lévy Noise

Abstract

We study the non-autonomous stochastic predator-prey model with Beddington-DeAngelies functional response driven by the system of stochastic differential equations with white noise, centered and non-centered Poisson noises. It is proved the existence and uniqueness of the global positive solution of considered system. We obtain sufficient conditions of stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak and strong persistence in the mean and extinction of the population densities in the considered stochastic predator-prey model.