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. © Springer-Verlag 2009.
Original language | English (US) |
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Pages (from-to) | 133-164 |
Number of pages | 32 |
Journal | Journal of Mathematical Biology |
Volume | 61 |
Issue number | 1 |
DOIs | |
State | Published - Aug 29 2009 |
Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: AM would like to acknowledge Professors Georg Hetzer and Wenxian Shen (Auburn University, USA) for fruitful discussions. EAG: This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). PKM was partially supported by a Royal Society Wolfson Merit Award.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.