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.
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Crampin, E.J., Gaffney, E.A. & Maini, P.K. Reaction and diffusion on growing domains: Scenarios for robust pattern formation. Bull. Math. Biol. 61, 1093–1120 (1999). https://doi.org/10.1006/bulm.1999.0131
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DOI: https://doi.org/10.1006/bulm.1999.0131