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

Handle URI:
http://hdl.handle.net/10754/599707
Title:
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Authors:
Madzvamuse, Anotida; Gaffney, Eamonn A.; Maini, Philip K.
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.
Citation:
Madzvamuse 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.
Publisher:
Springer Nature
Journal:
Journal of Mathematical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
29-Aug-2009
DOI:
10.1007/s00285-009-0293-4
PubMed ID:
19727733
Type:
Article
ISSN:
0303-6812; 1432-1416
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMadzvamuse, Anotidaen
dc.contributor.authorGaffney, Eamonn A.en
dc.contributor.authorMaini, Philip K.en
dc.date.accessioned2016-02-28T06:08:00Zen
dc.date.available2016-02-28T06:08:00Zen
dc.date.issued2009-08-29en
dc.identifier.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.en
dc.identifier.issn0303-6812en
dc.identifier.issn1432-1416en
dc.identifier.pmid19727733en
dc.identifier.doi10.1007/s00285-009-0293-4en
dc.identifier.urihttp://hdl.handle.net/10754/599707en
dc.description.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.en
dc.description.sponsorshipAM 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.en
dc.publisherSpringer Natureen
dc.subjectConvection-reaction-diffusion systemsen
dc.subjectDomain-induced diffusively-driven instabilityen
dc.subjectGrowing domains asymptotic theoryen
dc.subjectPattern formationen
dc.subjectTuring diffusively-driven instabilityen
dc.titleStability analysis of non-autonomous reaction-diffusion systems: the effects of growing domainsen
dc.typeArticleen
dc.identifier.journalJournal of Mathematical Biologyen
dc.contributor.institutionUniversity of Sussex, Sussex, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en

Related articles on PubMed

All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.