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

By D. L. Benson, P. K. Maini and J. A. Sherratt

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

Topics: Biology and other natural sciences
Year: 1993
DOI identifier: 10.1016/0895-7177(93)90025-T
OAI identifier: oai:generic.eprints.org:501/core69

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