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


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.


Pattern Formation Growth Function Pattern Selection Pattern Mode Domain Growth 
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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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