Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
KAUST Grant NumberKUK-C1-013-04
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AbstractBy 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.
CitationMadzvamuse A, Gaffney EA, Maini PK (2009) Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains. Journal of Mathematical Biology 61: 133–164. Available: http://dx.doi.org/10.1007/s00285-009-0293-4.
SponsorsAM 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.
JournalJournal of Mathematical Biology
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