IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v273y2016icp54-67.html
   My bibliography  Save this article

A three species dynamical system involving prey–predation, competition and commensalism

Author

Listed:
  • Gakkhar, Sunita
  • Gupta, Komal

Abstract

In this paper, a three species dynamical system is explored. The system consisting of two logistically growing competing species and the third species acts as a predator as well as host. It is predating over second species with Holling type II functional response, while first species is benefited from the third species. In addition, the prey species move into a refuge to avoid high predation. The essential mathematical features of the proposed model are studied in terms of boundedness, persistence, local stability and bifurcation. The existence of transcritical bifurcations have been established about two axial points. It has been observed that survival of all three species may be possible due to commensalism. Numerical simulations have been performed to show the Hopf bifurcation about interior equilibrium point. The existence of period-2 solution is observed. Further, the bifurcations of codimension-2 have also been investigated.

Suggested Citation

  • Gakkhar, Sunita & Gupta, Komal, 2016. "A three species dynamical system involving prey–predation, competition and commensalism," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 54-67.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:54-67
    DOI: 10.1016/j.amc.2015.09.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315012722
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.09.036?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. Flaaten, Ola, 1991. "Bioeconomics of sustainable harvest of competing species," Journal of Environmental Economics and Management, Elsevier, vol. 20(2), pages 163-180, March.
    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. Changhee Yoon & Seungyeon Moon & Heesang Lee, 2022. "Symbiotic Relationships in Business Ecosystem: A Systematic Literature Review," Sustainability, MDPI, vol. 14(4), pages 1-15, February.

    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. Eppink, Florian V. & van den Bergh, Jeroen C.J.M., 2007. "Ecological theories and indicators in economic models of biodiversity loss and conservation: A critical review," Ecological Economics, Elsevier, vol. 61(2-3), pages 284-293, March.
    2. Ola Flaaten & Kenneth Stollery, 1996. "The economic costs of biological predation," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 8(1), pages 75-95, July.
    3. Brodie, Jedediah F., 2018. "Carbon Costs and Bushmeat Benefits of Hunting in Tropical Forests," Ecological Economics, Elsevier, vol. 152(C), pages 22-26.
    4. Singh, Rajesh & Weninger, Quinn, 2007. "Economies of Scope in the Management of Mulitple Species Fisheries," Working Papers 7348, Iowa State University, Department of Economics.
    5. B. N. Obegi & I. Sarfo & G. N. Morara & P. Boera & E. Waithaka & A. Mutie, 2020. "Bio-economic modeling of fishing activities in Kenya: the case of Lake Naivasha Ramsar site," Journal of Bioeconomics, Springer, vol. 22(1), pages 15-31, April.
    6. N. Quérou & A. Tomini, 2018. "Marine Ecosystem Considerations and Second-Best Management," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 70(2), pages 381-401, June.
    7. Christine Bertram & Martin F. Quaas, 2017. "Biodiversity and Optimal Multi-species Ecosystem Management," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(2), pages 321-350, June.
    8. Kateregga, Eseza & Sterner, Thomas, 2008. "Lake Victoria Fish Stocks and the Effects of Water Hyacinths on the Catchability of Fish," RFF Working Paper Series dp-08-05-efd, Resources for the Future.
    9. Tibor Neugebauer, 2005. "Bioeconomics Of Sustainable Harvest Of Competing Species: A Comment," Others 0503012, University Library of Munich, Germany.
    10. Bertram, Christine, 2010. "Integrating biodiversity indices into a multi-species optimal control model," Kiel Working Papers 1662, Kiel Institute for the World Economy (IfW Kiel).
    11. Singh, Rajesh & Weninger, Quinn, 2009. "Bioeconomies of scope and the discard problem in multiple-species fisheries," Journal of Environmental Economics and Management, Elsevier, vol. 58(1), pages 72-92, July.
    12. Brock, W. A. & Xepapadeas, A., 2004. "Management of interacting species: regulation under nonlinearities and hysteresis," Resource and Energy Economics, Elsevier, vol. 26(2), pages 137-156, June.
    13. Stephen Kasperski, 2015. "Optimal Multi-species Harvesting in Ecologically and Economically Interdependent Fisheries," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 61(4), pages 517-557, August.
    14. Yajie Liu & Jon Olaf Olaussen & Anders Skonhoft, 2011. "When a Fish is a Fish: The Economic Impacts of Escaped Farmed Fish," Working Paper Series 12011, Department of Economics, Norwegian University of Science and Technology.
    15. Guillaume Bataille, 2024. "An Explicit Solution to Harvesting Behaviors in a Predator-Prey System," AMSE Working Papers 2405, Aix-Marseille School of Economics, France.
    16. Bella, Giovanni, 2007. "A Bug's Life: Competition Among Species Towards the Environment," Natural Resources Management Working Papers 10269, Fondazione Eni Enrico Mattei (FEEM).
    17. Carl-Erik Schulz, 1996. "Trade policy and ecology," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 8(1), pages 15-38, July.
    18. David Finnoff & John Tschirhart, 2003. "Protecting an Endangered Species While Harvesting Its Prey in a General Equilibrium Ecosystem Model," Land Economics, University of Wisconsin Press, vol. 79(2), pages 160-180.
    19. Giovanni Bella, 2007. "A Bug’s Life: Competition Among Species Towards the Environment," Working Papers 2007.18, Fondazione Eni Enrico Mattei.
    20. Frésard, Marjolaine & Ropars-Collet, Carole, 2014. "Sustainable harvest of a native species and control of an invasive species: A bioeconomic model of a commercial fishery invaded by a space competitor," Ecological Economics, Elsevier, vol. 106(C), pages 1-11.

    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:273:y:2016:i:c:p:54-67. 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.