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Survival analysis of an impulsive stochastic delay logistic model with Lévy jumps

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

Special Issues: Modeling and Complex Dynamics of Populations

This paper studies a stochastic delay logistic model with Lévy 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 Lévy jumps.
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Keywords persistence; Lévy 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 Lévy jumps. Mathematical Biosciences and Engineering, 2019, 16(5): 3251-3271. doi: 10.3934/mbe.2019162


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