The Mathematical Institute, University of Oxford, Eprints Archive

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

Madzvamuse, A. and Gaffney, E. A. and Maini, P. K. (2010) Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains. Journal of Mathematical Biology, 61 (1). pp. 133-164. ISSN n/a

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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.

Item Type:Article
Uncontrolled Keywords:Convection-reaction-diffusion systems - Turing diffusively-driven instability - Pattern formation - Growing domains asymptotic theory - Domain-induced diffusively-driven instability
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:922
Deposited By:Philip Maini
Deposited On:29 May 2010 09:16
Last Modified:29 May 2010 09:16

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