Persistence and extinction for stochastic logistic model with Lévy noise and impulsive perturbation

This article investigates a stochastic logistic model with Lévy noise and impulsive perturbation. In the model, the impulsive perturbation and Lévy noise are taken into account simultaneously. This model is new and more feasible and more accordance with the actual. The definition of solution to a stochastic differential equation with Lévy noise and impulsive perturba- tion is established. Based on this definition, we show that our model has a unique global positive solution and obtains its explicit expression. Sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained.