Crampin, E. J. and Gaffney, E. A. and Maini, P. K. (1999) Reaction and diffusion on growing domains: Scenarios for robust pattern formation. Bulletin of Mathematical Biology, 61 (6). pp. 1093-1120.
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.
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||23 Nov 2006|
|Last Modified:||20 Jul 2009 14:21|
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