Abstract
This paper investigates a stochastic Gilpin–Ayala model with general Levy jumps and stochastic perturbation to around the positive equilibrium of corresponding deterministic model. 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. Asymptotic behavior around the positive equilibrium of corresponding deterministic model is discussed. Our results imply the general Levy jumps is propitious to population survival when its intensity is more than 0, and some changes profoundly if not. Numerical simulink graphics are introduced to support the analytical findings.
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