IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v53y2022i2d10.1007_s13226-021-00117-5.html
   My bibliography  Save this article

Dynamics of predator-prey systems with prey’s dispersal between patches

Author

Listed:
  • Jiale Ban

    (Sun Yat-sen University)

  • Yuanshi Wang

    (Sun Yat-sen University)

  • Hong Wu

    (Sun Yat-sen University)

Abstract

This paper analyzes dispersal in predator-prey systems, where the prey can move between a source and a sink patch and the predation interaction is described by the Holling II functional response. By applying dynamical systems theory, we present a complete study on persistence of the system, and show local/global stability of equilibria. Then we prove Hopf bifurcation in the system by computing Lyapunov coefficient, and show that dispersal could lead to results reversing those if non-dispersing. By explicit expressions of stable equilibria, we show that dispersal could make the prey approach total abundance larger than if non-dispersing, even larger than its carrying capacity when the predator persists. Asymmetry in dispersal could also lead to the results. Total abundance of the prey is shown to be a distorted function (surface) of dispersal rates, which extends both previous theory and experimental observations. It is proven that there exists an optimal dispersal that drives the predator into extinction and makes the prey reach the maximal abundance. These results are biologically important in preserving endangered species.

Suggested Citation

  • Jiale Ban & Yuanshi Wang & Hong Wu, 2022. "Dynamics of predator-prey systems with prey’s dispersal between patches," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(2), pages 550-569, June.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:2:d:10.1007_s13226-021-00117-5
    DOI: 10.1007/s13226-021-00117-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-021-00117-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-021-00117-5?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. Goldwyn, Eli E. & Hastings, Alan, 2008. "When can dispersal synchronize populations?," Theoretical Population Biology, Elsevier, vol. 73(3), pages 395-402.
    2. Arditi, Roger & Lobry, Claude & Sari, Tewfik, 2018. "Asymmetric dispersal in the multi-patch logistic equation," Theoretical Population Biology, Elsevier, vol. 120(C), pages 11-15.
    3. Arditi, Roger & Lobry, Claude & Sari, Tewfik, 2015. "Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation," Theoretical Population Biology, Elsevier, vol. 106(C), pages 45-59.
    4. Wu, Hong & Wang, Yuanshi & Li, Yufeng & DeAngelis, Donald L., 2020. "Dispersal asymmetry in a two-patch system with source–sink populations," Theoretical Population Biology, Elsevier, vol. 131(C), pages 54-65.
    5. Ruiz-Herrera, Alfonso, 2018. "Metapopulation dynamics and total biomass: Understanding the effects of diffusion in complex networks," Theoretical Population Biology, Elsevier, vol. 121(C), pages 1-11.
    6. Huang, Rong & Wang, Yuanshi & Wu, Hong, 2020. "Population abundance in predator–prey systems with predator’s dispersal between two patches," Theoretical Population Biology, Elsevier, vol. 135(C), pages 1-8.
    7. Tiwari, Vandana & Tripathi, Jai Prakash & Mishra, Swati & Upadhyay, Ranjit Kumar, 2020. "Modeling the fear effect and stability of non-equilibrium patterns in mutually interfering predator–prey systems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu, Fei & Wang, Yuanshi, 2022. "Hopf bifurcation and Bautin bifurcation in a prey–predator model with prey’s fear cost and variable predator search speed," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 192-209.

    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. Huang, Rong & Wang, Yuanshi & Wu, Hong, 2020. "Population abundance in predator–prey systems with predator’s dispersal between two patches," Theoretical Population Biology, Elsevier, vol. 135(C), pages 1-8.
    2. Gao, Daozhou & Lou, Yuan, 2022. "Total biomass of a single population in two-patch environments," Theoretical Population Biology, Elsevier, vol. 146(C), pages 1-14.
    3. Sadykov, Alexander & Farnsworth, Keith D., 2021. "Model of two competing populations in two habitats with migration: Application to optimal marine protected area size," Theoretical Population Biology, Elsevier, vol. 142(C), pages 114-122.
    4. Wu, Hong & Wang, Yuanshi & Li, Yufeng & DeAngelis, Donald L., 2020. "Dispersal asymmetry in a two-patch system with source–sink populations," Theoretical Population Biology, Elsevier, vol. 131(C), pages 54-65.
    5. Auger, Pierre & Kooi, Bob & Moussaoui, Ali, 2022. "Increase of maximum sustainable yield for fishery in two patches with fast migration," Ecological Modelling, Elsevier, vol. 467(C).
    6. Wang, Yuanshi, 2019. "Asymmetric diffusion in a two-patch consumer-resource system," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 258-273.
    7. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    8. Tan, Chengguan & Wang, Yuanshi & Wu, Hong, 2020. "A consumer–resource system with source–sink populations and asymmetric dispersal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Jiapeng Qu & Zelin Liu & Zhenggang Guo & Yikang Li & Huakun Zhou, 2021. "A System Dynamics Model for Assessing the Efficacy of Lethal Control for Sustainable Management of Ochotona curzoniae on Tibetan Plateau," Sustainability, MDPI, vol. 13(2), pages 1-11, January.
    10. Arditi, Roger & Lobry, Claude & Sari, Tewfik, 2018. "Asymmetric dispersal in the multi-patch logistic equation," Theoretical Population Biology, Elsevier, vol. 120(C), pages 11-15.
    11. D.L. DeAngelis & Bo Zhang & Wei-Ming Ni & Yuanshi Wang, 2020. "Carrying Capacity of a Population Diffusing in a Heterogeneous Environment," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    12. Tripathi, Jai Prakash & Bugalia, Sarita & Burdak, Kavita & Abbas, Syed, 2021. "Dynamical analysis and effects of law enforcement in a social interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    13. Wang, Yuanshi & DeAngelis, Donald L., 2019. "Energetic constraints and the paradox of a diffusing population in a heterogeneous environment," Theoretical Population Biology, Elsevier, vol. 125(C), pages 30-37.
    14. Bagchi, Dweepabiswa & Arumugam, Ramesh & Chandrasekar, V.K. & Senthilkumar, D.V., 2022. "Metacommunity stability and persistence for predation turnoff in selective patches," Ecological Modelling, Elsevier, vol. 470(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:spr:indpam:v:53:y:2022:i:2:d:10.1007_s13226-021-00117-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.