Crampin, E. J. and Gaffney, E. A. and Maini, P. K. (2002) Mode doubling and tripling in reactiondiffusion patterns on growing domains: A piecewise linear model. Journal of Mathematical Biology, 44 (2). pp. 107128.

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Abstract
Reactiondiffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reactiondiffusion model generates a sequence of quasisteady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steadystate patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steadystate solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasisteady patterns in the sequence. We also highlight a novel sequence behaviour, modetripling, which is a consequence of a symmetry in the reaction term of the reactiondiffusion system.
Item Type:  Article 

Uncontrolled Keywords:  n/a 
Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Centre for Mathematical Biology 
ID Code:  399 
Deposited By:  Philip Maini 
Deposited On:  20 Nov 2006 
Last Modified:  29 May 2015 18:21 
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