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An Isaac Newton Institute Workshop

Pattern Formation in Growing omains

Interactions between pattern formation and domain growth

1st November 2005

Authors: Paul Matthews (Nottingham), Alex Neville (Nottingham), Helen Byrne (Nottingham)

Abstract

We develop a general framework for investigating pattern formation in reaction-diffusion systems for which the tissue on which the spatial pattern resides is growing at a rate which is regulated by the diffusible chemicals that establish the pattern. There is a complex interplay between the effects of the chemicals on the domain size and the influence of the domain size on the formation of patterns. The nature of this interaction is revealed by a weakly nonlinear analysis, which yields a pair of nonlinear equations for the amplitude of the spatial pattern and the domain size. The domain is found to grow (or shrink) at a rate that depends quadratically on the pattern amplitude.