Turing pattern formation with fractional diffusion and fractional reactions

Article

Langlands, T. A. M., Henry, B. I. and Wearne, S. L.. 2006. "Turing pattern formation with fractional diffusion and fractional reactions." Journal of Physics: Condensed Matter. 19 (6), pp. 065115 -065134. https://doi.org/10.1088/0953-8984/19/6/065115
Article Title

Turing pattern formation with fractional diffusion and fractional reactions

ERA Journal ID1110
Article CategoryArticle
AuthorsLanglands, T. A. M. (Author), Henry, B. I. (Author) and Wearne, S. L. (Author)
Journal TitleJournal of Physics: Condensed Matter
Journal Citation19 (6), pp. 065115 -065134
Number of Pages20
Year2006
Place of PublicationUnited Kingdom
ISSN0953-8984
1361-648X
Digital Object Identifier (DOI)https://doi.org/10.1088/0953-8984/19/6/065115
Web Address (URL)https://iopscience.iop.org/article/10.1088/0953-8984/19/6/065115
Abstract

We have investigated Turing pattern formation through linear stability analysis and numerical simulations in a two-species reaction–diffusion system in which a fractional order temporal derivative operates on both species, and on both the diffusion term and the reaction term. The order of the fractional derivative affects the time onset of patterning in this model system but it does not affect critical parameters for the onset of Turing instabilities and it does not affect the final spatial pattern. These results contrast with earlier studies of Turing pattern formation in fractional reaction–diffusion systems with a fractional order temporal derivative on the diffusion term but not the reaction term.
In addition to elucidating differences between these two model systems, our studies provide further evidence that Turing linear instability analysis is an excellent predictor of both the onset of and the nature of pattern formation in fractional nonlinear reaction–diffusion equations.

Keywordsanomoalous subdiffusion, fractional reaction diffusion equation, Turing pattern formation
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020340607. Reaction kinetics and dynamics
490410. Partial differential equations
490101. Approximation theory and asymptotic methods
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Byline AffiliationsUniversity of New South Wales
Icahn School of Medicine at Mount Sinai, United States
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