Population dynamical behaviors of stochastic logistic system with jumps

This paper is concerned with a stochastic logistic model driven by martingales with jumps. In the model, generalized noise and jump noise are taken into account. This model is new and more feasible. The explicit global positive solution of the system is presented, and then sufficient conditions for extinction and persistence are established. The critical value of extinction, nonpersistence in the mean, and weak persistence in the mean are obtained. The path-wise and moment properties are also investigated. Finally, some simulation figures are introduced to illustrate the main results.