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

Mischler, Stéphane; Quiñinao, Cristóbal; Weng, Qilong (2018), Weak and strong connectivity regimes for a general time elapsed neuron network model. https://basepub.dauphine.fr/handle/123456789/17936

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NeuronDiscontG.pdf (357.2Kb)
Type
Document de travail / Working paper
External document link
https://hal-univ-diderot.archives-ouvertes.fr/hal-01703349
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
20
Metadata
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Author(s)
Mischler, Stéphane
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Quiñinao, Cristóbal
Departamento de Ingeniería Matemática [Santiago] [DIM]
Weng, Qilong
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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].
Subjects / Keywords
neuron network

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