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Bulletin of Mathematical Biology

, Volume 61, Issue 6, pp 1093–1120 | Cite as

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

  • Edmund J. CrampinEmail author
  • Eamonn A. Gaffney
  • Philip K. Maini
Article

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.

Keywords

Pattern Formation Growth Function Pattern Selection Pattern Mode Domain Growth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Society for Mathematical Biology 1999

Authors and Affiliations

  • Edmund J. Crampin
    • 1
    Email author
  • Eamonn A. Gaffney
    • 1
  • Philip K. Maini
    • 1
  1. 1.Centre for Mathematical BiologyMathematical InstituteOxfordUK

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