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hal.structure.identifierGroup for Neural Theory [Paris]
dc.contributor.authorDUMONT, Gregory
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorHENRY, Jacques
hal.structure.identifierFaculty of Computer Science [Iași]
dc.contributor.authorTARNICERIU, Carmen Oana
dc.date.accessioned2024-04-04T03:12:18Z
dc.date.available2024-04-04T03:12:18Z
dc.date.issued2016
dc.identifier.issn0303-6812
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193855
dc.description.abstractEnProviding an analytical treatment to the stochastic feature of neu-rons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire model and its associated Fokker-Planck equation are probably the most popular way to deal with neural variability. Another well-known formalism is the escape-rate model: a model giving the probability that a neuron fires at a certain time knowing the time elapsed since its last action potential. This model leads to a so-called age-structured system, a partial differential equation with non-local boundary condition famous in the field of population dynamics, where the age of a neuron is the amount of time passed by since its previous spike. In this theoretical paper, we investigate the mathematical connection between the two formalisms. We shall derive an integral transform of the solution to the age-structured model into the solution of the Fokker-Planck equation. This integral transform highlights the link between the two stochastic processes. As far as we know, an explicit mathematical correspondence between the two solutions has not been introduced until now.
dc.language.isoen
dc.publisherSpringer
dc.title.enNoisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model
dc.typeArticle de revue
dc.identifier.doi10.1007/s00285-016-1002-8
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv1512.03785
bordeaux.journalJournal of Mathematical Biology
bordeaux.page1413 - 1436
bordeaux.volume73
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01414588
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01414588v1
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