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Reaction and diffusion on growing domains: Scenarios for robust pattern formation

By E. J. Crampin, E. A. Gaffney and P. K. Maini

Abstract

We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence of patterns for exponential domain growth and we find numerically that frequency-doubling is realized for a finite range of exponential growth rate. We consider pattern formation under different forms for the growth and show that in one dimension domain growth may be a mechanism for increased robustness of pattern formation

Topics: Biology and other natural sciences
Year: 1999
DOI identifier: 10.1006/bulm.1999.0131
OAI identifier: oai:generic.eprints.org:423/core69
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