IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i9p1812-1818.html
   My bibliography  Save this article

Turing bifurcation in a reaction–diffusion system with density-dependent dispersal

Author

Listed:
  • Kumar, Niraj
  • Horsthemke, Werner

Abstract

Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of dispersal. We perform a linear stability analysis of the uniform steady state to find the conditions for the Turing bifurcation and compare it with the standard Turing condition in a reaction–diffusion system, where dispersal is described by simple Fickian diffusion. While activator–inhibitor kinetics are a necessary condition for the Turing instability as in standard two-variable systems, the instability can occur even if the diffusion constant of the inhibitor is equal to or smaller than that of the activator. We apply these results to two model systems, the Brusselator and the Gierer–Meinhardt model.

Suggested Citation

  • Kumar, Niraj & Horsthemke, Werner, 2010. "Turing bifurcation in a reaction–diffusion system with density-dependent dispersal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1812-1818.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:9:p:1812-1818
    DOI: 10.1016/j.physa.2009.12.052
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437109010668
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2009.12.052?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. Muolo, Riccardo & Gallo, Luca & Latora, Vito & Frasca, Mattia & Carletti, Timoteo, 2023. "Turing patterns in systems with high-order interactions," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    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:phsmap:v:389:y:2010:i:9:p:1812-1818. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.