Repository logo
 
Publication

Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations

2015Journal article Restricted access
Simple item page
dc.contributor.authorMadzvamuse, Anotida
dc.contributor.authorNdakwo, Hussaini
dc.contributor.authorBarreira, Raquel
dc.date.accessioned2018-04-09T13:25:46Z
dc.date.available2018-04-09T13:25:46Z
dc.date.issued2015
dc.description.abstractBy introducing linear cross-diffusion for a two-component reaction-diffusion system withactivator-depletedreaction kinetics (Gierer and Meinhardt,Kybernetik 12:30–39,1972;PrigogineandLefever,JChemPhys48:1695–1700,1968;Schnakenberg, J Theor Biol 81:389–400,1979), we derivecross-diffusion-driveninstability conditions and show that they are a generalisation of the classical diffusion-driveninstabilityconditionsintheabsenceofcross-diffusion.Ourmostrevealingresultis that, in contrast to the classical reaction-diffusion systems without cross-diffusion,it is no longer necessary to enforce that one of the species diffuse much faster than theother.Furthermore,it is no longer necessary to have an activator–inhibitor mecha-nism as premises for pattern formation, activator–activator,inhibitor–inhibitorreac-tion kinetics as well asshort-range inhibitionandlong-range activationall have thepotential of giving rise to cross-diffusion-driven instability. To support our theoreti-cal findings, we compute cross-diffusion induced parameter spaces and demonstratesimilarities and differences to those obtained using standard reaction-diffusion theory.Finite element numerical simulations on planary square domains are presented to back-up theoretical predictions. For the numerical simulations presented, we choose parameter values from and outside the classical Turing diffusively-driven instability space;outside, these are chosen to belong to cross-diffusively-driven instability parameterspaces. Our numerical experiments validate our theoretical predictions that parameterspaces induced by cross-diffusion in both theuandvcomponents of the reaction-diffusion system are substantially larger and different from those without cross-diffusion. Furthermore, the parameter spaces without cross-diffusion are sub-spacesof the cross-diffusion induced parameter spaces. Our results allow experimentalists tohave a wider range of parameter spaces from which to select reaction kinetic parametervalues that will give rise to spatial patterning in the presence of cross-diffusion.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationMadzvamuse A., Ndakwo, H.S. , Barreira, R. (2015) Cross-diffusion-driven instability for reaction-diffusion systems: Analysis and simulations. J. Math. Biol., 70, pp. 709-743. doi: 10.1007/s00285-014-0779-6pt_PT
dc.identifier.doi10.1007/s00285-014-0779-6pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.26/22217
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.subjectCross-diffusion reaction systemspt_PT
dc.subjectCross-diffusion driven instabilitypt_PT
dc.subjectParameter space identificationpt_PT
dc.subjectPattern formationpt_PT
dc.subjectPlanary domainspt_PT
dc.subjectFinite element methodpt_PT
dc.titleCross-diffusion-driven instability for reaction-diffusion systems: analysis and simulationspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.titleJournal of Mathematical Biologypt_PT
person.familyNameBarreira
person.givenNameRaquel
person.identifier.ciencia-id011B-AC27-378A
person.identifier.orcid0000-0002-8326-1593
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication11adc260-5103-4d3a-887f-6ae77108f173
relation.isAuthorOfPublication.latestForDiscovery11adc260-5103-4d3a-887f-6ae77108f173

Files

Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
JMB_Madzvamuse_Ndakwo_Barreira_2015.pdf
Size:
4.45 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.85 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

IPS - ESTB - SMG - Artigos científicos