Turing pattern formation with fractional diffusion and fractional reactions

Langlands, T. A. M. and Henry, B. I. and Wearne, S. L. (2006) Turing pattern formation with fractional diffusion and fractional reactions. Journal of Physics: Condensed Matter, 19 (6). 065115 -065134. ISSN 0953-8984

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Depositing User: Dr Trevor Langlands
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 30 Oct 2009 10:04
Last Modified: 26 Sep 2013 05:30
Uncontrolled Keywords: anomoalous subdiffusion, fractional reaction diffusion equation, Turing pattern formation
Fields of Research (FOR2008): 03 Chemical Sciences > 0307 Theoretical and Computational Chemistry > 030703 Reaction Kinetics and Dynamics
01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1088/0953-8984/19/6/065115
URI: http://eprints.usq.edu.au/id/eprint/5442

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