IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v495y2018icp294-311.html
   My bibliography  Save this article

Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise

Author

Listed:
  • Wang, Sheng
  • Wang, Linshan
  • Wei, Tengda

Abstract

This paper concerns the dynamics of a stochastic predator–prey system with Markovian switching and Lévy noise. First, the existence and uniqueness of global positive solution to the system is proved. Then, by combining stochastic analytical techniques with M-matrix analysis, sufficient conditions of stochastic permanence and extinction are obtained. Furthermore, for the stochastic permanence case, by means of four constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated. Finally, our conclusions are illustrated through an example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:495:y:2018:i:c:p:294-311
    DOI: 10.1016/j.physa.2017.12.088
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117313389
    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.2017.12.088?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. Wan, Li & Zhou, Qinghua, 2009. "Stochastic Lotka-Volterra model with infinite delay," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 698-706, 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.
    4. Ouyang, Mengqian & Li, Xiaoyue, 2015. "Permanence and asymptotical behavior of stochastic prey–predator system with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 539-559.
    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. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    8. Xiangjun Dai & Hui Jiao & Jianjun Jiao & Qi Quan, 2023. "Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    9. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    10. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 199-210.
    11. Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.
    12. Sheng Wang & Guixin Hu & Linshan Wang, 2018. "Stability in Distribution of a Stochastic Competitive Lotka-Volterra System with S-type Distributed Time Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1241-1257, December.
    13. 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.
    14. 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.
    15. 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.
    16. Sheng Wang & Lijuan Dong, 2024. "Dynamics of a Stochastic Regime-Switching Four-Species Food Chain Model with Distributed Delays and Harvesting," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-15, September.
    17. 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.
    18. Wang, Sheng & Hu, Guixin & Wei, Tengda & Wang, Linshan, 2018. "Stability in distribution of a stochastic predator–prey system with S-type distributed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 919-930.
    19. 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.
    20. 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:495:y:2018:i:c:p:294-311. 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.