Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.26/22217 |
Resumo: | By 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. |
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Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulationsCross-diffusion reaction systemsCross-diffusion driven instabilityParameter space identificationPattern formationPlanary domainsFinite element methodBy 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.Repositório ComumMadzvamuse, AnotidaNdakwo, HussainiBarreira, Raquel2018-04-09T13:25:46Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.26/22217engMadzvamuse 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/s00285-014-0779-610.1007/s00285-014-0779-6metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-21T09:53:41Zoai:comum.rcaap.pt:10400.26/22217Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:09:37.000621Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations |
title |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations |
spellingShingle |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations Madzvamuse, Anotida Cross-diffusion reaction systems Cross-diffusion driven instability Parameter space identification Pattern formation Planary domains Finite element method |
title_short |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations |
title_full |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations |
title_fullStr |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations |
title_full_unstemmed |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations |
title_sort |
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations |
author |
Madzvamuse, Anotida |
author_facet |
Madzvamuse, Anotida Ndakwo, Hussaini Barreira, Raquel |
author_role |
author |
author2 |
Ndakwo, Hussaini Barreira, Raquel |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Comum |
dc.contributor.author.fl_str_mv |
Madzvamuse, Anotida Ndakwo, Hussaini Barreira, Raquel |
dc.subject.por.fl_str_mv |
Cross-diffusion reaction systems Cross-diffusion driven instability Parameter space identification Pattern formation Planary domains Finite element method |
topic |
Cross-diffusion reaction systems Cross-diffusion driven instability Parameter space identification Pattern formation Planary domains Finite element method |
description |
By 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. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015 2015-01-01T00:00:00Z 2018-04-09T13:25:46Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.26/22217 |
url |
http://hdl.handle.net/10400.26/22217 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Madzvamuse 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/s00285-014-0779-6 10.1007/s00285-014-0779-6 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799135358847287296 |