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Weak and strong connectivity regimes for a general time elapsed neuron network model

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NeuronDiscontG.pdf (357.2Kb)
Date
2018
Publishing date
03-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal-univ-diderot.archives-ouvertes.fr/hal-01703349
Dewey
Analyse
Sujet
neuron network
URI
https://basepub.dauphine.fr/handle/123456789/17936
Collections
  • CEREMADE : Publications
Metadata
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Author
Mischler, Stéphane
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Quiñinao, Cristóbal
18014 Departamento de Ingeniería Matemática [Santiago] [DIM]
Weng, Qilong
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
20
Abstract (EN)
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works [7, 8, 6], we establish accurate estimate on the long time behavior of the solutions in the weak and the strong connectivity regime both in the case with and without delay. Our results improve [7, 8] where a less accurate estimate was established and [6] where only smooth firing rates were considered. Our approach combines several arguments introduced in the above previous works as well as a slightly refined version of the Weyl's and spectral mapping theorems presented in [13, 4].

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