IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v515y2019icp355-375.html
   My bibliography  Save this article

Stochastic mutualism model under regime switching with Lévy jumps

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118313207
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.09.189?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.
    10. 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.
    11. Gao, Miaomiao & Jiang, Daqing, 2019. "Analysis of stochastic multimolecular biochemical reaction model with lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 601-613.
    12. Wu, Jian, 2018. "Stability of a three-species stochastic delay predator–prey system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 492-505.
    13. 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.
    14. Wu, Jian, 2020. "Dynamics of a two-predator one-prey stochastic delay model with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:355-375. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.