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The threshold of stochastic Gilpin–Ayala model subject to general Lévy jumps

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Abstract

This paper investigates a stochastic Gilpin–Ayala model with general Lévy jumps and stochastic perturbation to around the positive equilibrium of corresponding deterministic model. 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. Asymptotic behavior around the positive equilibrium of corresponding deterministic model is discussed. Our results imply the general Lévy jumps is propitious to population survival when its intensity is more than 0, and some changes profoundly if not. Numerical simulink graphics are introduced to support the analytical findings.

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Authors and Affiliations

  1. Department of Mathematics, Qingdao University of Technology, Qingdao, 266520, China

    Chun Lu, Lijuan Chen & Yumin Wang

  2. Department of Mechinery and Electric, Qingdao Technical College, Qingdao, 266555, China

    Shan Gao

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  1. Chun Lu
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  2. Lijuan Chen
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  3. Yumin Wang
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  4. Shan Gao
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Correspondence to Lijuan Chen.

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This work was supported by grants from the Natural Science Foundation of Shandong Province of China (Nos. ZR2018MA023 and ZR2017MA008), a Project of Shandong Province Higher Educational Science and Technology Program of China (Nos.J16LI09 and J18KA218), National Natural Science Foundation of China (No. 61803220).

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Lu, C., Chen, L., Wang, Y. et al. The threshold of stochastic Gilpin–Ayala model subject to general Lévy jumps. J. Appl. Math. Comput. 60, 731–747 (2019). https://doi.org/10.1007/s12190-018-01234-x

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  • DOI: https://doi.org/10.1007/s12190-018-01234-x

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