Abstract
Lévy noise, accounting for sudden catastrophic shocks, exists widely in the natural world. However, the effect of Lévy noise on the survival of a population is not well understood. In this paper, we develop and investigate a stochastic competitive model of two species with Lévy noise in an impulsive polluted environment. The threshold between weak persistence in the mean and extinction is established for each species. Sufficient conditions for strong persistence in the mean, stability in the mean and stochastic permanence are obtained. These results show that Lévy noise can change the persistence and extinction of each species significantly. Numerical simulations is carried out to illustrate the theoretical results.
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