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Stochastic Predator-Prey System Subject to Lévy Jumps

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  • Xinzhu Meng
  • Xiaohong Wang

Abstract

This paper investigates a new nonautonomous impulsive stochastic predator-prey system with the omnivorous predator. First, we show that the system has a unique global positive solution for any given initial positive value. Second, the extinction of the system under some appropriate conditions is explored. In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. Simulations are also carried out to illustrate our theoretical analysis conclusions.

Suggested Citation

  • Xinzhu Meng & Xiaohong Wang, 2016. "Stochastic Predator-Prey System Subject to Lévy Jumps," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-13, March.
    • Handle: RePEc:hin:jnddns:5749892
    DOI: 10.1155/2016/5749892
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    Cited by:

    1. Zhuo, Xiao-jing & Guo, Yong-feng & Qi, Jing-yan & Wang, Qian-qian, 2024. "Stationary distribution and mean extinction time in a generalist prey–predator model driven by Lévy noises," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).

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