Dynamics of logistic systems driven by Lévy noise under regime switching

This article concerns the stochastic logistic models under regime switching with Lévy noise. In the model, the color noise and Lévy noise are taken into account at the same time. This model is new and more feasible and more accordance with the actual. Some dynamical behaviors are investigated and sufficient conditions for stochastic permanence, extinction, non-persistence in the mean and weak persistence are established. The critical value among the extinction, non-persistence in the mean and weak persistence is obtained. Our results demonstrate that the asymptotic properties of the model have close relations with the Lévy noise and stationary distribution of the color noise.