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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierEcole Polytechnique Fédérale de Lausanne [EPFL]
dc.contributor.authorRUIZ-BAIER, Ricardo
hal.structure.identifierYancheng Institute of Technology [YIT]
dc.contributor.authorTIAN, Canrong
dc.date.accessioned2024-04-04T03:12:49Z
dc.date.available2024-04-04T03:12:49Z
dc.date.issued2016
dc.identifier.issn0303-6812
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193899
dc.description.abstractEnWe focus our attention on the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population superdiffusion. First, we address the weak solvability of the coupled problem employing the Faedo-Galerkin method and compactness arguments. In addition, we are interested in how cross superdiffusion influences the formation of spatial patterns: a linear stability analysis has been carried out, showing that cross superdiffusion triggers Turing instabilities, whereas classical self superdiffusion suppresses Turing instability. We have also performed a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume (MRFV) method that employs shifted Grunwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators, and aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.
dc.language.isoen
dc.publisherSpringer
dc.subject.enTuring instability
dc.subject.enPattern formation
dc.subject.enAmplitude equations
dc.subject.enSuperdiffusion
dc.subject.enFinite volume approximation
dc.subject.enFully adaptive multiresolution
dc.subject.enPhD Yangzhou
dc.subject.enJiangsu Province CHINA Corresponding Author Secondary Information: Corresponding Author's Institution: Corresponding Author's Secondary Institution:
dc.title.enTuring pattern dynamics and adaptive discretization for a superdiffusive Lotka-Volterra system
dc.typeArticle de revue
dc.subject.halMathématiques [math]
bordeaux.journalJournal of Mathematical Biology
bordeaux.page1441-1465
bordeaux.volume6
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01403081
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01403081v1
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