Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 76, pp. 1-16.

Title: Dynamics of logistic systems driven by Levy noise under regime switching

Authors: Ruihua Wu    (Harbin Institute of Technology, Weihai, China)
         Xiaoling Zou (Harbin Institute of Technology, Weihai, China)
         Ke Wang      (Harbin Institute of Technology, Weihai, China)

Abstract:
 This article concerns the stochastic logistic models under regime
 switching with Levy noise. In the model, the color noise and Levy
 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 Levy noise and
 stationary distribution of the color noise.

Submitted December 4, 2013. Published March 19, 2014.
Math Subject Classifications: 60H10, 60J75, 60J28.
Key Words: Logistic equation; Markov chain; Levy noise; extinction;
           stochastic permanence.