The Mathematical Institute, University of Oxford, Eprints Archive

Diffusion driven instability in an inhomogeneous domain

Benson, D. L. and Sherratt, J. A. and Maini, P. K. (1993) Diffusion driven instability in an inhomogeneous domain. Bulletin of Mathematical Biology, 55 (2). pp. 365-384.

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Abstract

Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.

Item Type:Article
Uncontrolled Keywords:n/a
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:512
Deposited By:Philip Maini
Deposited On:13 Dec 2006
Last Modified:20 Jul 2009 14:22

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