The Mathematical Institute, University of Oxford, Eprints Archive

Pattern formation in spatially heterogeneous Turing reaction-diffusion models

Page, K. and Maini, P. K. and Monk, N. A. M. (2003) Pattern formation in spatially heterogeneous Turing reaction-diffusion models. Physica D, 181 (1-2). pp. 80-101.

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Abstract

The Turing reaction–diffusion model [Phil. Trans. R. Soc. 237 (1952) 37–72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially homogeneous parameters. The case of parameters which vary spatially has received less attention. Here, we show that a simple step function heterogeneity in a kinetic parameter can lead to spatial pattern formation outside the classical Turing space parameter regime for patterning. This reduces the constraints on the model parameters, extending possible applications. Furthermore, it highlights the potential importance of boundaries during pattern formation.

Item Type:Article
Uncontrolled Keywords:Pattern formation; Turing reaction–diffusion models; Self-organised spatial pattern
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:380
Deposited By:Philip Maini
Deposited On:17 Nov 2006
Last Modified:20 Jul 2009 14:20

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