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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.

Type

Journal article

Journal

Bull Math Biol

Publication Date

11/1999

Volume

61

Pages

1093 - 1120

Keywords

Algorithms, Animals, Body Patterning, Growth, Humans, Kinetics, Models, Biological