IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/5293748.html
   My bibliography  Save this article

Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type

Author

Listed:
  • Lianchao Gu
  • Peiliang Gong
  • Hongqing Wang

Abstract

The reaction diffusion system is one of the important models to describe the objective world. It is of great guiding importance for people to understand the real world by studying the Turing patterns of the reaction diffusion system changing with the system parameters. Therefore, in this paper, we study Gierer–Meinhardt model of the Depletion type which is a representative model in the reaction diffusion system. Firstly, we investigate the stability of the equilibrium and the Hopf bifurcation of the system. The result shows that equilibrium experiences a Hopf bifurcation in certain conditions and the Hopf bifurcation of this system is supercritical. Then, we analyze the system equation with the diffusion and study the impacts of diffusion coefficients on the stability of equilibrium and the limit cycle of system. Finally, we perform the numerical simulations for the obtained results which show that the Turing patterns are either spot or stripe patterns.

Suggested Citation

  • Lianchao Gu & Peiliang Gong & Hongqing Wang, 2020. "Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-10, January.
    • Handle: RePEc:hin:jnddns:5293748
    DOI: 10.1155/2020/5293748
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/DDNS/2020/5293748.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/DDNS/2020/5293748.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/5293748?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shi, Yao & Wu, Jianhua & Wang, Yan’e, 2021. "Qualitative analysis for a biological depletion model," Applied Mathematics and Computation, Elsevier, vol. 401(C).

    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:hin:jnddns:5293748. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.