✦ LIBER ✦

Reaction and Diffusion on Growing Domains: Scenarios for Robust Pattern Formation

✍ Scribed by Edmund J. Crampin; Eamonn A. Gaffney; Philip K. Maini

Publisher: Springer
Year: 1999
Tongue: English
Weight: 783 KB
Volume: 61
Category: Article
ISSN: 1522-9602
DOI: 10.1006/bulm.1999.0131

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✦ Synopsis

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.

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