Electron. J. Diff. Equ., Vol. 2014 (2014), No. 76, pp. 1-16.

Dynamics of logistic systems driven by Levy noise under regime switching

Ruihua Wu, Xiaoling Zou, Ke Wang

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.

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Ruihua Wu
Department of Mathematics
Harbin Institute of Technology, Weihai 264209, China.
College of Science, China University of Petroleum (East China)
Qingdao 266555, China
email: wu_ruihua@hotmail.com, wu_ruihua@upc.edu.cn
Xiaoling Zou
Department of Mathematics, Harbin Institute of Technology
Weihai 264209, China
email: zouxiaoling1025@126.com
Ke Wang
Department of Mathematics
Harbin Institute of Technology
Weihai 264209, China
email: w_k@hotmail.com

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