
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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Type
Document de travail / Working paperExternal document link
https://hal-univ-diderot.archives-ouvertes.fr/hal-01703349Date
2018Series title
Cahier de recherche CEREMADE, Université Paris-DauphinePages
20
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Show full item recordAuthor(s)
Mischler, StéphaneCEntre 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 networkRelated items
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Mischler, Stéphane; Weng, Qilong (2018) Article accepté pour publication ou publié
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Mischler, Stéphane; Weng, Qilong (2017) Article accepté pour publication ou publié
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Mischler, Stéphane; Quiñinao, Cristóbal; Touboul, Jonathan (2016) Article accepté pour publication ou publié