The Mathematical Institute, University of Oxford, Eprints Archive

Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients

Benson, D. L. and Maini, P. K. and Sherratt, J. A. (1993) Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients. Mathematical and Computer Modelling, 17 (12). pp. 29-34.

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Abstract

We consider a reaction diffusion system in one spatial dimension in which the diffusion coefficients are spatially varying. We present a non-standard linear analysis for a certain class of spatially varying diffusion coefficients and show that it accurately predicts the behaviour of the full nonlinear system near bifurcation. We show that the steady state solutions exhibit qualitatively different behaviour to that observed in the usual case with constant diffusion coefficients. Specifically, the modified system can generate patterns with spatially varying amplitude and wavelength. Application to chondrogenesis in the limb is discussed.

Item Type:Article
Uncontrolled Keywords:n/a
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:501
Deposited By:Philip Maini
Deposited On:12 Dec 2006
Last Modified:20 Jul 2009 14:21

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