IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i18p3838-d1235105.html
   My bibliography  Save this article

Survival Analysis of a Predator–Prey Model with Seasonal Migration of Prey Populations between Breeding and Non-Breeding Regions

Author

Listed:
  • Xiangjun Dai

    (School of Date Science, Tongren University, Tongren 554300, China
    School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

  • Hui Jiao

    (School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China)

  • Jianjun Jiao

    (School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Qi Quan

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

Abstract

In this paper, we establish and study a novel predator–prey model that incorporates: (i) the migration of prey between breeding and non-breeding regions; (ii) the refuge effect of prey; and (iii) the reduction in prey pulse birth rate, in the form of a fear effect, in the presence of predators. Applying the Floquet theory and the comparison theorem of impulsive differential equations, we obtain the sufficient conditions for the stability of the prey-extinction periodic solution and the permanence of the system. Furthermore, we also study the case where the prey population does not migrate. Sufficient conditions for the stability of the prey-extinction periodic solution and the permanence are also established, and the threshold for extinction and permanence of the prey population is obtained. Finally, some numerical simulations are provided to verify the theoretical results. These results provide a theoretical foundation for the conservation of biodiversity.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3838-:d:1235105
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/18/3838/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/18/3838/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wang, Limin & Liu, Zhijun & Jinghui, & Chen, Lansun, 2007. "Impulsive diffusion in single species model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1213-1219.
    2. Li Zu & Daqing Jiang & Donal O’Regan, 2014. "Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, January.
    3. Xiaoling Zou & Dejun Fan & Ke Wang, 2013. "Effects of Dispersal for a Logistic Growth Population in Random Environments," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, March.
    4. Zijian Liu & Chenxue Yang, 2015. "Permanence and Periodic Solutions for a Two-Patch Impulsive Migration Periodic -Species Lotka-Volterra Competitive System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-14, December.
    5. Lingzhi Huang & Zhichun Yang, 2015. "Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-9, May.
    6. 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.
    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. 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.
    2. 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).
    3. Jiao, Jianjun & Yang, Xiaosong & Cai, Shaohong & Chen, Lansun, 2009. "Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 522-532.
    4. 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.
    5. 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.
    6. Xie, Youxiang & Wang, Linjun & Deng, Qicheng & Wu, Zhengjia, 2017. "The dynamics of an impulsive predator–prey model with communicable disease in the prey species only," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 320-335.
    7. Ayoubi, Tawfiqullah & Bao, Haibo, 2020. "Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 386(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:gam:jmathe:v:11:y:2023:i:18:p:3838-:d:1235105. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.