IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v384y2020ics0096300320303489.html
   My bibliography  Save this article

Optimality for a diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge

Author

Listed:
  • Liu, Guodong
  • Chang, Zhengbo
  • Meng, Xinzhu
  • Liu, Siyu

Abstract

In this paper, we consider the optimal harvesting controls for a diffusive predator-prey system, which is formulated by prey refuge and modified Leslie-Gower functional response. The locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous Neumann boundary condition. The nonexistence and existence of nonconstant steady states are obtained by Leray-Schauder degree theory. Also, the optimal harvesting strategies to get maximum sustainable yield (MSY) and maximum economic yield (MEY) are correspondingly given.

Suggested Citation

  • Liu, Guodong & Chang, Zhengbo & Meng, Xinzhu & Liu, Siyu, 2020. "Optimality for a diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    • Handle: RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320303489
    DOI: 10.1016/j.amc.2020.125385
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320303489
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125385?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. Legović, Tarzan & Klanjšček, Jasminka & Geček, Sunčana, 2010. "Maximum sustainable yield and species extinction in ecosystems," Ecological Modelling, Elsevier, vol. 221(12), pages 1569-1574.
    2. Liu, Guodong & Meng, Xinzhu, 2019. "Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(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. Ma, Tingting & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2021. "Stability analysis and optimal harvesting control of a cross-diffusion prey-predator system," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Jang, Geunsoo & Cho, Giphil, 2022. "Optimal harvest strategy based on a discrete age-structured model with monthly fishing effort for chub mackerel, Scomber japonicus, in South Korea," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Arellano-García, María Evarista & Camacho-Gutiérrez, José Ariel & Solorza-Calderón, Selene, 2021. "Machine learning approach for higher-order interactions detection to ecological communities management," Applied Mathematics and Computation, Elsevier, vol. 411(C).

    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. Legović, Tarzan & Geček, Sunčana, 2010. "Impact of maximum sustainable yield on independent populations," Ecological Modelling, Elsevier, vol. 221(17), pages 2108-2111.
    2. Móréh, Ágnes & Endrédi, Anett & Piross, Sándor Imre & Jordán, Ferenc, 2021. "Topology of additive pairwise effects in food webs," Ecological Modelling, Elsevier, vol. 440(C).
    3. Adhikary, Prabir Das & Mukherjee, Saikat & Ghosh, Bapan, 2021. "Bifurcations and hydra effects in Bazykin’s predator–prey model," Theoretical Population Biology, Elsevier, vol. 140(C), pages 44-53.
    4. Woodall, Hannah & Bullock, James M. & White, Steven M., 2014. "Modelling the harvest of an insect pathogen," Ecological Modelling, Elsevier, vol. 287(C), pages 16-26.
    5. Barman, Binandita & Ghosh, Bapan, 2019. "Explicit impacts of harvesting in delayed predator-prey models," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 213-228.
    6. Ghosh, Bapan & Kar, T.K., 2014. "Sustainable use of prey species in a prey–predator system: Jointly determined ecological thresholds and economic trade-offs," Ecological Modelling, Elsevier, vol. 272(C), pages 49-58.
    7. Rajni, & Ghosh, Bapan, 2022. "Multistability, chaos and mean population density in a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    8. Legović, Tarzan & Geček, Sunčana, 2012. "Impact of maximum sustainable yield on mutualistic communities," Ecological Modelling, Elsevier, vol. 230(C), pages 63-72.
    9. Das, Debabrata & Kar, T.K. & Pal, Debprasad, 2023. "The impact of invasive species on some ecological services in a harvested predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 66-90.
    10. Kar, T.K. & Ghosh, Bapan, 2013. "Impacts of maximum sustainable yield policy to prey–predator systems," Ecological Modelling, Elsevier, vol. 250(C), pages 134-142.

    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:384:y:2020:i:c:s0096300320303489. 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.