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Mathematical Biosciences and Engineering, 2019, 16(5): 3251-3271. doi: 10.3934/mbe.2019162. Research article Special Issues

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Survival analysis of an impulsive stochastic delay logistic model with L´evy jumps

Chun Lu, Bing Li, Limei Zhou, Liwei Zhang

1 Department of Mathematics, Qingdao University of Technology, Qingdao, 266520, P.R. China
2 School of Mathematical Science, Harbin Normal University, Harbin, 150025, P.R. China
3 School of Civil Engineering, Qingdao University of Technology, Qingdao, 266520, P.R. China

Received: , Accepted: , Published:

Special Issues: Modeling and Complex Dynamics of Populations

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This paper studies a stochastic delay logistic model with L´evy jumps and impulsive perturbations. We show that the model has a unique global positive solution. Suﬃcient conditions for extinction, non-persistence in the mean, weak persistence, stochastic permanence and global asymptotic stability are established. The threshold between weak persistence and extinction is obtained. The results demonstrate that impulsive perturbations which may represent human factor play an important role in protecting the population even if it suﬀers sudden environmental shocks that can be discribed by L´evy jumps.

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Keywords: persistence ; L´evy jump ; impulsive perturbation ; logistic model ; inﬁnite delay

Citation: Chun Lu, Bing Li, Limei Zhou, Liwei Zhang. Survival analysis of an impulsive stochastic delay logistic model with L´evy jumps. Mathematical Biosciences and Engineering, 2019, 16(5): 3251-3271. doi: 10.3934/mbe.2019162

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