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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.

Original publication

DOI

10.1007/s00285-009-0293-4

Type

Journal article

Journal

J Math Biol

Publication Date

07/2010

Volume

61

Pages

133 - 164

Keywords

Diffusion, Growth, Kinetics, Models, Biological, Models, Chemical, Models, Statistical