IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n835310.html

Hopf Bifurcation and Global Periodic Solutions in a Predator‐Prey System with Michaelis‐Menten Type Functional Response and Two Delays

Author

Listed:
  • Yunxian Dai
  • Yiping Lin
  • Huitao Zhao

Abstract

We consider a predator‐prey system with Michaelis‐Menten type functional response and two delays. We focus on the case with two unequal and non‐zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delays τ1 ≠ τ2.

Suggested Citation

  • Yunxian Dai & Yiping Lin & Huitao Zhao, 2014. "Hopf Bifurcation and Global Periodic Solutions in a Predator‐Prey System with Michaelis‐Menten Type Functional Response and Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:835310
    DOI: 10.1155/2014/835310
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/835310
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/835310?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
    ---><---

    References listed on IDEAS

    as
    1. Hu, Guang-Ping & Li, Wan-Tong & Yan, Xiang-Ping, 2009. "Hopf bifurcations in a predator–prey system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1273-1285.
    2. Ming Zhao, 2013. "Hopf Bifurcation Analysis for a Semiratio‐Dependent Predator‐Prey System with Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Ming Zhao, 2013. "Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, September.
    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. Debao Gao, 2022. "Dynamic System Analysis of Investment in Both Production and R&D with Time Delay," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

    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. Xinhong Pan & Min Zhao & Chuanjun Dai & Yapei Wang, 2014. "Stability and Hopf Bifurcation Analysis of a Nutrient‐Phytoplankton Model with Delay Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    3. Tang, Xiaosong, 2022. "Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 420-429.
    4. Bilazeroğlu, Ş. & Göktepe, S. & Merdan, H., 2023. "Effects of the random walk and the maturation period in a diffusive predator–prey system with two discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. Barman, Dipesh & Kumar Upadhyay, Ranjit, 2026. "Impact of carryover and fear-induced delays on population dynamics: A cross-model stability and bifurcation investigation," Applied Mathematics and Computation, Elsevier, vol. 516(C).
    6. Mishra, P. & Raw, S.N. & Tiwari, B., 2019. "Study of a Leslie–Gower predator-prey model with prey defense and mutual interference of predators," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 1-16.
    7. Pati, N.C. & Ghosh, Bapan, 2022. "Delayed carrying capacity induced subcritical and supercritical Hopf bifurcations in a predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 171-196.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:835310. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.