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Well-Posedness and Asymptotic Behaviors for a Predator-Prey System with Lévy Noise

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Listed:
  • Sheng Wang

    (Ocean University of China)

  • Linshan Wang

    (Ocean University of China)

  • Tengda Wei

    (Ocean University of China)

Abstract

In this paper, well-posedness and asymptotic behaviors for a predator-prey system with Lévy noise are studied by using stochastic analytical techniques. Firstly, the existence and uniqueness of positive global solution with positive initial value is proved. Then, stochastic permanence for the system is investigated. Finally, persistence in mean and extinction for the system are discussed and some numerical simulations are provided to support our results.

Suggested Citation

  • Sheng Wang & Linshan Wang & Tengda Wei, 2017. "Well-Posedness and Asymptotic Behaviors for a Predator-Prey System with Lévy Noise," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 715-725, September.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-016-9509-4
    DOI: 10.1007/s11009-016-9509-4
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    References listed on IDEAS

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    1. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    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.
    3. Liu, Meng & Deng, Meiling & Du, Bo, 2015. "Analysis of a stochastic logistic model with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 169-182.
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