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Dynamics of a stochastic Holling II one-predator two-prey system with jumps

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  • Zhang, Xinhong
  • Li, Wenxue
  • Liu, Meng
  • Wang, Ke

Abstract

In this paper, a stochastic Holling II one-predator two-prey system with jumps is investigated. Firstly, the properties of the solution, such as the existence and uniqueness of the global positive solution, stochastic ultimate boundedness and the pathwise estimation are studied. Then we mainly establish the sufficient conditions for the extinction and persistence in the mean of the solution. Results show that positive jump noise is advantageous to the system while negative jump noise is disadvantageous. Finally, a numerical example is introduced to illustrate the results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:571-582
    DOI: 10.1016/j.physa.2014.11.060
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    Cited by:

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    2. Guodong Liu & Xiaohong Wang & Xinzhu Meng & Shujing Gao, 2017. "Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps," Complexity, Hindawi, vol. 2017, pages 1-15, June.
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    5. Jaouad Danane & Delfim F. M. Torres, 2023. "Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species," Mathematics, MDPI, vol. 11(7), pages 1-22, March.
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    9. Shao, Yuanfu, 2022. "Global stability of a delayed predator–prey system with fear and Holling-type II functional response in deterministic and stochastic environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 65-77.
    10. 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.
    11. Liu, Lidan & Meng, Xinzhu & Zhang, Tonghua, 2017. "Optimal control strategy for an impulsive stochastic competition system with time delays and jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 99-113.
    12. Wang, Sheng & Wang, Linshan & Wei, Tengda, 2018. "Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 294-311.
    13. 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.
    14. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2020. "Permanence of hybrid competitive Lotka–Volterra system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    15. Liu, Meng & Bai, Chuanzhi & Deng, Meiling & Du, Bo, 2016. "Analysis of stochastic two-prey one-predator model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 176-188.
    16. Yang, Ruizhi, 2017. "Bifurcation analysis of a diffusive predator–prey system with Crowley–Martin functional response and delay," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 131-139.

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