Reaction and diffusion on growing domains: scenarios for robust pattern formation.
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.
Crampin
E J
EJ
Centre for Mathematical Biology, Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, UK. crampin@maths.ox.ac.uk
Gaffney
E A
EA
Maini
P K
PK
D000465:Algorithms; D000818:Animals; D019521:Body Patterning / Q000502:physiology*; D006128:Growth / Q000502:physiology; D006801:Humans; D007700:Kinetics; D008954:Models, Biological