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Diffusion driven instability in an inhomogeneous circular domain
journal contribution
posted on 2023-05-18, 19:05 authored by May, A, Firby, PA, Andrew BassomAndrew BassomClassical reaction-diffusion systems have been extensively studied and are now well understood. Most of the work to date has been concerned with homogeneous models within one-dimensional or rectangular domains. However, it is recognised that in most applications nonhomogeneity, as well as other geometries, are typically more important. In this paper, we present a two chemical reaction-diffusion process which is operative within a circular region and the model is made nonhomogeneous by supposing that one of the diffusion coefficients varies with the radial variable. Linear analysis leads to the derivation of a dispersion relation for the point of onset of instability and our approach enables both axisymmetric and nonaxisymmetric modes to be described. We apply our workings to the standard Schnackenberg activator-inhibitor model in the case when the variable diffusion coefficient takes on a step-function like profile. Some fully nonlinear simulations show that the linear analysis captures the essential details of the behaviour of the model.
History
Publication title
Mathematical and Computer ModellingVolume
29Issue
4Pagination
53-66ISSN
0895-7177Department/School
School of Natural SciencesPublisher
Pergamon-Elsevier Science LtdPlace of publication
The Boulevard, Langford Lane, Kidlington, Oxford, England, Ox5 1GbRights statement
Copyright 1999 ElsevierRepository Status
- Restricted