Global-in-time behavior of the solution to a Gierer-Meinhardt system

Georgia Karali*, Takashi Suzuki, Yoshio Yamada

*この研究の対応する著者

    研究成果: Article査読

    16 被引用数 (Scopus)

    抄録

    Gierer-Meinhardt system is a mathematical model to describe biological pattern formation due to activator and inhibitor. Turing pattern is expected in the presence of local self-enhancement and long-range inhibition. The long-time behavior of the solution, however, has not yet been clarified mathematically. In this paper, we study the case when its ODE part takes periodic-in-time solutions, that is, τ = s+1/p-1 . Under some additional assumptions on parameters, we show that the solution exists global-in-time and absorbed into one of these ODE orbits. Thus spatial patterns eventually disappear if those parameters are in a region without local self-enhancement or long-range inhibition.

    本文言語English
    ページ(範囲)2885-2900
    ページ数16
    ジャーナルDiscrete and Continuous Dynamical Systems- Series A
    33
    7
    DOI
    出版ステータスPublished - 2013 7月

    ASJC Scopus subject areas

    • 離散数学と組合せ数学
    • 応用数学
    • 分析

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