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

Article English OPEN
Chun Lu ; Qiang Ma ; Xiaohua Ding (2015)
  • Publisher: Texas State University
  • Journal: Electronic Journal of Differential Equations (issn: 1072-6691)
  • Subject: Logistic equation | Levy noise | impulsive perturbation | stochastic permanence | Mathematics | QA1-939

This article investigates a stochastic logistic model with Levy noise and impulsive perturbation. In the model, the impulsive perturbation and Levy 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 Levy noise and impulsive perturbation 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.
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