IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v361y2019icp258-273.html
   My bibliography  Save this article

Asymmetric diffusion in a two-patch consumer-resource system

Author

Listed:
  • Wang, Yuanshi

Abstract

This paper considers a two-patch system with consumer diffusion, which characterizes laboratory experiments and includes exploitable resources. Using dynamical systems theory, we exhibit global dynamics of the one-patch subsystem and show existence of stable positive equilibria in the two-patch system. Based on rigorous analysis, we demonstrate that heterogeneously distributed resources with asymmetric diffusion can support higher total population abundance than those with symmetric diffusion, or without diffusion. A novel finding of this work is that the asymmetric diffusion can make heterogeneously distributed resources support higher total population abundance than homogeneously distributed resources, even with species diffusion, which extends previous theory. Meanwhile, we reveal that intermediate asymmetry is favorable for total population abundance, while extremely large or extremely small asymmetry is unfavorable. Our results are consistent with experimental observations and provide new insights. Numerical simulations confirm and extend the results.

Suggested Citation

  • Wang, Yuanshi, 2019. "Asymmetric diffusion in a two-patch consumer-resource system," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 258-273.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:258-273
    DOI: 10.1016/j.amc.2019.05.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319304370
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.05.035?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. 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.
    2. Wang, Yuanshi, 2018. "Global dynamics of a competition–parasitism–mutualism model characterizing plant–pollinator–robber interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 26-41.
    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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. Benaïm, Michel & Lobry, Claude & Sari, Tewfik & Strickler, Édouard, 2023. "Untangling the role of temporal and spatial variations in persistence of populations," Theoretical Population Biology, Elsevier, vol. 154(C), pages 1-26.
    10. 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.
    11. 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.

    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:361:y:2019:i:c:p:258-273. 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.