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

Anotida Madzvamuse, Eamonn A. Gaffney, Philip K. Maini

Research output: Contribution to journalArticlepeer-review

73 Scopus citations

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 languageEnglish (US)
Pages (from-to)133-164
Number of pages32
JournalJournal of Mathematical Biology
Volume61
Issue number1
DOIs
StatePublished - Aug 29 2009
Externally publishedYes

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