The Mathematical Institute, University of Oxford, Eprints Archive

Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients

Maini, P. K. and Benson, D. L. and Sherratt, J. A. (1992) Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients. IMA Journal of Mathematics Applied in Medicine & Biology, 9 (3). pp. 197-213.

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Abstract

Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the existence of spatial inhomogeneities in various biological systems, most models have only been considered in a spatially homogeneous environment. The authors consider a two-chemical reaction-diffusion mechanism in one space dimension in which one of the diffusion coefficients depends explicitly on the spatial variable. The model is analysed in the case of a step function diffusion coefficient and the insight gained for this special case is used to discuss pattern generation for smoothly varying diffusion coefficients. The results show that spatial inhomogeneity may be an important biological pattern regulator, and possible applications of the model to chondrogenesis in the vertebrate limb are suggested.

Item Type:Article
Uncontrolled Keywords:diffusion-driven instability • pattern isolation • inhomogeneous environment • development hierarchy
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:509
Deposited By:Philip Maini
Deposited On:13 Dec 2006
Last Modified:20 Jul 2009 14:21

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