IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v271y2015icp418-428.html
   My bibliography  Save this article

Asymptotic behavior of a stochastic non-autonomous predator-prey system with jumps

Author

Listed:
  • Liu, Qun
  • Chen, Qingmei

Abstract

In this paper, a two-species stochastic non-autonomous food chain predator-prey system with jumps is proposed and studied. The asymptotic properties of the system are examined. Sufficient conditions for extinction, non-persistence in the mean, weak persistence in the mean and weak persistence of the system are established. Results show that Lévy jumps are disadvantageous for the persistence of the populations. Furthermore, we also show that the solution is stochastically ultimate bounded under certain conditions. Some examples together with numerical simulations are introduced to illustrate our main results.

Suggested Citation

  • Liu, Qun & Chen, Qingmei, 2015. "Asymptotic behavior of a stochastic non-autonomous predator-prey system with jumps," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 418-428.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:418-428
    DOI: 10.1016/j.amc.2015.08.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315010954
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.08.040?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. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    2. 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.
    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. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li, 2019. "Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 894-907.
    2. Yang, Jiangtao, 2020. "Threshold behavior in a stochastic predator–prey model with general functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    4. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    5. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    6. Peng Luo & Falei Wang, 2019. "Viability for Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(1), pages 395-416, March.
    7. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    8. 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.
    9. Romuald Elie & Emma Hubert & Thibaut Mastrolia & Dylan Possamai, 2019. "Mean-field moral hazard for optimal energy demand response management," Papers 1902.10405, arXiv.org, revised Mar 2020.
    10. Frank Bosserhoff & Mitja Stadje, 2019. "Robustness of Delta Hedging in a Jump-Diffusion Model," Papers 1910.08946, arXiv.org, revised Apr 2022.
    11. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    12. Liu, Qun & Jiang, Daqing, 2020. "Dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    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. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution and extinction of a stochastic HIV-1 model with Beddington–DeAngelis infection rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 414-426.
    15. Zhao, Dianli, 2015. "A remark on one non-autonomous stochastic Gompertz model with delay," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 369-373.
    16. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    17. Vadillo, Fernando, 2019. "Comparing stochastic Lotka–Volterra predator-prey models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 181-189.
    18. Zuo, Wenjie & Jiang, Daqing & Sun, Xinguo & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Long-time behaviors of a stochastic cooperative Lotka–Volterra system with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 542-559.
    19. El Fatini, Mohamed & El Khalifi, Mohamed & Gerlach, Richard & Laaribi, Aziz & Taki, Regragui, 2019. "Stationary distribution and threshold dynamics of a stochastic SIRS model with a general incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    20. Wen, Buyu & Rifhat, Ramziya & Teng, Zhidong, 2019. "The stationary distribution in a stochastic SIS epidemic model with general nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 258-271.

    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:apmaco:v:271:y:2015:i:c:p:418-428. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.