The Mathematical Institute, University of Oxford, Eprints Archive

Mode transitions in a model reaction-diffusion system driven by domain growth and noise

Barrass, I. and Crampin, E. J. and Maini, P. K. (2006) Mode transitions in a model reaction-diffusion system driven by domain growth and noise. Bulletin of Mathematical Biology, 68 (5). pp. 981-995.

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Abstract

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns.

Item Type:Article
Uncontrolled Keywords:Turing model - Schnakenberg - Spatial pattern - Robustness - Mode-doubling failure - Mode selection
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:319
Deposited By:Philip Maini
Deposited On:08 Nov 2006
Last Modified:20 Jul 2009 14:20

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