A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics

Bruno Cessac 1, 2
2 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (``raster plots''). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.
Type de document :
Article dans une revue
Journal of Mathematical Biology, Springer Verlag (Germany), 2008, 56 (3), pp.311-345
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https://hal.inria.fr/inria-00423350
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Soumis le : vendredi 9 octobre 2009 - 15:41:08
Dernière modification le : mardi 24 avril 2018 - 17:20:11

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  • HAL Id : inria-00423350, version 1
  • ARXIV : 0706.0077

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Bruno Cessac. A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics. Journal of Mathematical Biology, Springer Verlag (Germany), 2008, 56 (3), pp.311-345. 〈inria-00423350〉

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