Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 247, pp. 1-14.
Persistence and extinction for stochastic logistic model with Levy
noise and impulsive perturbation
Chun Lu, Qiang Ma, Xiaohua Ding
Abstract:
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.
Submitted September 5, 2014. Published September 23, 2015.
Math Subject Classifications: 64H10, 60J75, 35R12.
Key Words: Logistic equation; Levy noise; impulsive perturbation;
stochastic permanence
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Chun Lu
Department of Mathematics
Qingdao Technological University
Qingdao 266520, China
email: mathlc@163.com
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Qiang Ma
Department of Mathematics
Harbin Institute of Technology
Weihai 264209, China
email: hitmaqiang@hotmail.com
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Xiaohua Ding
Department of Mathematics
Harbin Institute of Technology
Weihai 264209, China
email: mathlc@126.com
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