Abstract
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.
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Madzvamuse, A., Gaffney, E.A. & Maini, P.K. Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains. J. Math. Biol. 61, 133–164 (2010). https://doi.org/10.1007/s00285-009-0293-4
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DOI: https://doi.org/10.1007/s00285-009-0293-4
Keywords
- Convection-reaction-diffusion systems
- Turing diffusively-driven instability
- Pattern formation
- Growing domains asymptotic theory
- Domain-induced diffusively-driven instability