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Stochastic mutualism model under regime switching with Lévy jumps

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  • Gao, Hongjun
  • Wang, Ying

Abstract

This paper is concerned with a stochastic mutualism model under regime switching with Lévy jumps. To begin with, the existence and uniqueness of the global positive solution is proved with any given positive initial value. Then, the sufficient conditions for stochastic permanence are established. The critical value between extinction and persistence in mean is also obtained. In addition, under some suitable conditions, we proved that there is a unique stationary distribution for the system without Lévy jumps. Our method relies on the Lyapunov function analysis and the Fredholm alternative. The results demonstrate that regime switching may contribute to the permanence but jump noise may suppress the permanence.

Suggested Citation

  • Gao, Hongjun & Wang, Ying, 2019. "Stochastic mutualism model under regime switching with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 355-375.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:355-375
    DOI: 10.1016/j.physa.2018.09.189
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    References listed on IDEAS

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    1. Guo, Yingjia, 2017. "Stochastic regime switching SIR model driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 1-11.
    2. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
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