Dynamics analysis of a stochastic non-autonomous one-predator–two-prey system with Beddington–DeAngelis functional response and impulsive perturbations

In this paper, we explore a stochastic non-autonomous one-predator–two-prey system with Beddington–DeAngelis functional response and impulsive perturbations. First, by using Ito’s formula, exponential martingale inequality, Chebyshev’s inequality and other mathematical skills, we establish some sufficient conditions for extinction, non-persistence in the mean, weak persistence, persistence in the mean and stochastic permanence of the solution of the stochastic system. Then the limit of the average in time of the sample path of the solution is estimated by two constants. Afterwards, the lower-growth rate and the upper-growth rate of the positive solution are estimated. In addition, sufficient conditions for global attractivity of the system are established. Finally, we carry out some simulations to verify our main results and explain the biological implications: the large stochastic interference is disadvantageous for the persistence of the population and the strong impulsive harvesting can lead to extinct of the population.