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.
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.
|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|
|Deposited By:||Philip Maini|
|Deposited On:||13 Dec 2006|
|Last Modified:||20 Jul 2009 14:21|
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