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Relaxation in time elapsed neuron network models in the weak connectivity regime

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorMischler, Stéphane*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorWeng, Qilong*
dc.date.accessioned2017-12-01T10:34:55Z
dc.date.available2017-12-01T10:34:55Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17138
dc.language.isoenen
dc.subjectNeuron networks
dc.subjecttime elapsed dynamics
dc.subjectsemigroup spectral analysis
dc.subjectweak connectivity
dc.subjectlong time asymptotic
dc.subject.ddc515en
dc.titleRelaxation in time elapsed neuron network models in the weak connectivity regime
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since the last discharge. Under general assumption on the firing rate and the delay distribution, we prove the uniqueness of the steady state and its nonlinear exponential stability in the weak connectivity regime. The result generalizes some similar results obtained in [10] in the case without delay. Our approach uses the spectral analysis theory for semigroups in Banach spaces developed recently by the first author and collaborators.
dc.relation.isversionofjnlnameActa Applicandae Mathematicae
dc.relation.isversionofjnlvol157
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages45-74
dc.relation.isversionofdoi10.1007/s10440-018-0163-4
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01148645
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-20T15:05:17Z
hal.author.functionaut
hal.author.functionaut


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