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Asymptotic and transient behaviour for a nonlocal problem arising in population genetics

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBURIE, Jean-Baptiste
hal.structure.identifierSanté et agroécologie du vignoble [UMR SAVE]
dc.contributor.authorDJIDJOU-DEMASSE, R
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDUCROT, Arnaud
dc.date.accessioned2024-04-04T03:05:13Z
dc.date.available2024-04-04T03:05:13Z
dc.date.issued2020
dc.identifier.issn0956-7925
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193225
dc.description.abstractEnThis work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. First we study the asymptotic behaviour of the system and prove that it eventually converges to a stationary state. Next we more closely investigate the behaviour of the system in the presence of multiple evolutionary attractors. Under suitable assumptions and based on a small mutation variance asymptotic, we describe the existence of a long transient regime during which the pathogen population remains far from its asymptotic behaviour and highly concentrated around some phenotypic value that is different from the one described by its asymptotic behaviour. In that setting, the time needed for the system to reach its large time configuration is very long and multiple evolutionary attractors may act as a barrier of evolution that can be very long to bypass.
dc.language.isoen
dc.publisherCambridge University Press (CUP)
dc.subject.enasymptotic behaviour
dc.subject.enNonlocal equation
dc.subject.enpopulation genetics
dc.subject.entransient behaviour
dc.title.enAsymptotic and transient behaviour for a nonlocal problem arising in population genetics
dc.typeArticle de revue
dc.identifier.doi10.1017/S0956792518000487
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halSciences du Vivant [q-bio]/Génétique/Génétique des populations [q-bio.PE]
bordeaux.journalEuropean Journal of Applied Mathematics
bordeaux.page84-110
bordeaux.volume31
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01874125
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01874125v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=European%20Journal%20of%20Applied%20Mathematics&rft.date=2020&rft.volume=31&rft.issue=1&rft.spage=84-110&rft.epage=84-110&rft.eissn=0956-7925&rft.issn=0956-7925&rft.au=BURIE,%20Jean-Baptiste&DJIDJOU-DEMASSE,%20R&DUCROT,%20Arnaud&rft.genre=article


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