On the pattern formation mechanism of (2 + 1)D max-plus models

Daisuke Takahashi, Atsuhiko Shida, Motohiro Usami

    Research output: Contribution to journal › Article

    7 Citations (Scopus)

    Abstract

    We propose a max-plus equation which reproduces evolutional patterns often observed in reaction-diffusion systems of excitable media. The equation gives a travelling wave, a target pattern and a spiral pattern from appropriate initial data. Moreover, using the advantages of max-plus equations, we obtain the solutions exactly by a reduction from the high-dimensional equation to a lower one. In the reduction, we use coordinate curves according to a pattern shape. It is interesting that all patterns satisfy the same reduced equation. We also propose two other models similar to the previous one and discuss the behaviour of solutions.

    Original languageEnglish
    Pages (from-to)10715-10726
    Number of pages12
    JournalJournal of Physics A: Mathematical and General
    Volume34
    Issue number48
    DOIs
    Publication statusPublished - 2001 Dec 7

    Fingerprint

    Pattern Formation
    Excitable Media
    Model
    Behavior of Solutions
    Reaction-diffusion System
    traveling waves
    Traveling Wave
    High-dimensional
    Curve
    Target
    curves

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics

    Cite this

    On the pattern formation mechanism of (2 + 1)D max-plus models. / Takahashi, Daisuke; Shida, Atsuhiko; Usami, Motohiro.

    In: Journal of Physics A: Mathematical and General, Vol. 34, No. 48, 07.12.2001, p. 10715-10726.

    Research output: Contribution to journal › Article

    Takahashi, D, Shida, A & Usami, M 2001, 'On the pattern formation mechanism of (2 + 1)D max-plus models', Journal of Physics A: Mathematical and General, vol. 34, no. 48, pp. 10715-10726. https://doi.org/10.1088/0305-4470/34/48/333
    Takahashi D, Shida A, Usami M. On the pattern formation mechanism of (2 + 1)D max-plus models. Journal of Physics A: Mathematical and General. 2001 Dec 7;34(48):10715-10726. https://doi.org/10.1088/0305-4470/34/48/333
    Takahashi, Daisuke ; Shida, Atsuhiko ; Usami, Motohiro. / On the pattern formation mechanism of (2 + 1)D max-plus models. In: Journal of Physics A: Mathematical and General. 2001 ; Vol. 34, No. 48. pp. 10715-10726.
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