IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n704320.html

Hopf Bifurcation Control in a Delayed Predator‐Prey System with Prey Infection and Modified Leslie‐Gower Scheme

Author

Listed:
  • Zizhen Zhang
  • Huizhong Yang

Abstract

Hopf bifurcation of a delayed predator‐prey system with prey infection and the modified Leslie‐Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifurcation in the system. In addition, direction of Hopf bifurcation and stability of the bifurcated periodic solutions of the controlled system are obtained by using normal form and center manifold theory. Finally, numerical simulation results are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation.

Suggested Citation

  • Zizhen Zhang & Huizhong Yang, 2013. "Hopf Bifurcation Control in a Delayed Predator‐Prey System with Prey Infection and Modified Leslie‐Gower Scheme," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:704320
    DOI: 10.1155/2013/704320
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/704320
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/704320?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. Guo, Hongjian & Song, Xinyu, 2008. "An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1320-1331.
    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. Hai-Feng Huo & Zhan-Ping Ma & Chun-Ying Liu, 2009. "Persistence and Stability for a Generalized Leslie‐Gower Model with Stage Structure and Dispersal," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    2. Zou, Xiaoling & Li, Qingwei & Cao, Wenhao & Lv, Jingliang, 2023. "Thresholds and critical states for a stochastic predator–prey model with mixed functional responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 780-795.
    3. Xiao, Qizhen & Dai, Binxiang, 2015. "Dynamics of an impulsive predator–prey logistic population model with state-dependent," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 220-230.
    4. Jianglin Zhao & Yong Yan, 2016. "Dynamics of a Seasonally Forced Phytoplankton‐Zooplankton Model with Impulsive Biological Control," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    5. Guo, Hongjian & Chen, Lansun & Song, Xinyu, 2009. "Dynamic analysis of a kind of species control model concerning impulsively releasing pathogen and infective predator," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1326-1336.

    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:704320. 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.