IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n495072.html

Hopf Bifurcation Analysis for a Semiratio‐Dependent Predator‐Prey System with Two Delays

Author

Listed:
  • Ming Zhao

Abstract

This paper is concerned with a semiratio‐dependent predator‐prey system with nonmonotonic functional response and two delays. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Change of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a sequence of critical values. The properties of Hopf bifurcation such as direction and stability are determined by using the normal form method and center manifold theorem. Numerical simulations confirm our theoretical findings.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:495072
    DOI: 10.1155/2013/495072
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/495072
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/495072?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. Shuang Guo & Weihua Jiang, 2012. "Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, March.
    2. Shuang Guo & Weihua Jiang, 2012. "Hopf Bifurcation Analysis on General Gause‐Type Predator‐Prey Models with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    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. 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).
    2. 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).

    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. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.

    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:2013:y:2013:i:1:n:495072. 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.