Extinction and persistence of a nonautonomous stochastic food-chain system with impulsive perturbations

In this paper, a nonautonomous stochastic food-chain system with functional response and impulsive perturbations is studied. By using Ito’s formula, exponential martingale inequality, differential inequality and other mathematical skills, some sufficient conditions for the extinction, nonpersistence in the mean, persistence in the mean, and stochastic permanence of the system are established. Furthermore, some asymptotic properties of the solutions are also investigated. Finally, a series of numerical examples are presented to support the theoretical results, and effects of different intensities of white noises perturbations and impulsive effects are discussed by the simulations.