Reaction and diffusion on growing domains: Scenarios for robust pattern formation
- 846 Downloads
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.
KeywordsPattern Formation Growth Function Pattern Selection Pattern Mode Domain Growth
Unable to display preview. Download preview PDF.
- Crampin, E. J., E. A. Gaffney, W. W. Hackborn and P. K. Maini. Reaction—diffusion patterns on growing domains: asymmetric growth. (In preparation.)Google Scholar
- Lacalli, T. C., D. A. Wilkinson and L. G. Harrison (1988). Theoretical aspects of stripe formation in relation to Drosophila segmentation. Development 103, 105–113.Google Scholar
- Murray, J. D. (1993). Mathematical Biology, volume 19 of Biomathematics Texts, 2nd edn, Berlin and London: Springer-Verlag.Google Scholar
- Turing, A. M. (1952). The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237, 37–72.Google Scholar