Asymptotic and transient behaviour for a nonlocal problem arising in population genetics
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BURIE, Jean-Baptiste | |
| hal.structure.identifier | Santé et agroécologie du vignoble [UMR SAVE] | |
| dc.contributor.author | DJIDJOU-DEMASSE, R | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DUCROT, Arnaud | |
| dc.date.accessioned | 2024-04-04T03:05:13Z | |
| dc.date.available | 2024-04-04T03:05:13Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 0956-7925 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193225 | |
| dc.description.abstractEn | This 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.iso | en | |
| dc.publisher | Cambridge University Press (CUP) | |
| dc.subject.en | asymptotic behaviour | |
| dc.subject.en | Nonlocal equation | |
| dc.subject.en | population genetics | |
| dc.subject.en | transient behaviour | |
| dc.title.en | Asymptotic and transient behaviour for a nonlocal problem arising in population genetics | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1017/S0956792518000487 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Sciences du Vivant [q-bio]/Génétique/Génétique des populations [q-bio.PE] | |
| bordeaux.journal | European Journal of Applied Mathematics | |
| bordeaux.page | 84-110 | |
| bordeaux.volume | 31 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01874125 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01874125v1 | |
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