IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921008328.html
   My bibliography  Save this article

Turing-Hopf bifurcation analysis and normal form of a diffusive Brusselator model with gene expression time delay

Author

Listed:
  • Lv, Yehu
  • Liu, Zhihua

Abstract

In this paper, by incorporating the gene expression time delay into a diffusive Brusselator model, a diffusive Brusselator model with gene expression time delay is proposed, and the Turing-Hopf bifurcation of the proposed model subject to homogeneous Neumann boundary condition is investigated. Firstly, the condition for the occurrence of Turing instability is deduced, and the existence of Turing bifurcation, Hopf bifurcation and Turing-Hopf bifurcation for the proposed model is also established. Then by a slight modification, the normal form on the center manifold near the Turing-Hopf singularity for the proposed model is derived by using the algorithm of calculating the normal form of Turing-Hopf bifurcation for the general reaction diffusion system with delay. With the aid of the obtained third-order truncated normal form of the proposed model, the spatiotemporal dynamics corresponding to six different regions in the parameter plane are analyzed. Moreover, by the corresponding relationships between the equilibrium points of the normal form and the solutions of original system, the dynamics of the original system can also be obtained. Finally, some numerical simulations are carried out to support the theoretical findings.

Suggested Citation

  • Lv, Yehu & Liu, Zhihua, 2021. "Turing-Hopf bifurcation analysis and normal form of a diffusive Brusselator model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921008328
    DOI: 10.1016/j.chaos.2021.111478
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008328
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111478?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.

    Citations

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


    Cited by:

    1. Lv, Yehu, 2022. "The spatially homogeneous hopf bifurcation induced jointly by memory and general delays in a diffusive system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Hassan Y. Alfifi & Saad M. Almuaddi, 2024. "Stability Analysis and Hopf Bifurcation for the Brusselator Reaction–Diffusion System with Gene Expression Time Delay," Mathematics, MDPI, vol. 12(8), pages 1-19, April.
    3. Yang, Rui, 2022. "Turing–Hopf bifurcation co-induced by cross-diffusion and delay in Schnakenberg system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Zhang, Xiaofeng & Yuan, Rong, 2022. "Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and weak kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 56-70.

    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:chsofr:v:152:y:2021:i:c:s0960077921008328. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.