Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains.
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth.
Madzvamuse
Anotida
A
Department of Mathematics, University of Sussex, Mantell Building, Brighton, BN1 9RF, UK. a.madzvamuse@sussex.ac.uk
Gaffney
Eamonn A
EA
Maini
Philip K
PK
D004058:Diffusion; D006128:Growth; D007700:Kinetics; D008954:Models, Biological; D008956:Models, Chemical; D015233:Models, Statistical