Deviation from the predicted wavenumber in a mode selection problem for the Turing patterns

In this paper, we investigate a mode selection problem for the Turing patterns generated from small random initial disturbances in one-dimensional reaction-diffusion systems on a sufficiently large domain. For this problem, it is widely accepted that the maximizer of the dispersion relation give ris...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2008-10, Vol.25 (3), p.281-303
Main Author: Kuwamura, Masataka
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
dispersion relation
Heuristic
Mathematics
Mathematics and Statistics
mode selection
Studies
Turing pattern
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Summary:In this paper, we investigate a mode selection problem for the Turing patterns generated from small random initial disturbances in one-dimensional reaction-diffusion systems on a sufficiently large domain. For this problem, it is widely accepted that the maximizer of the dispersion relation give rise to the wavenumber to be selected. Even in a small neighborhood of the bifurcation point, our numerical experiments show that this is not always true.
ISSN:0916-7005
1868-937X
DOI:10.1007/BF03168552