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

2 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique - ENS Paris, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS-PSL - 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.
Document type :
Journal articles
Domain :

https://hal.inria.fr/inria-00423350
Contributor : Alain Monteil Connect in order to contact the contributor
Submitted on : Friday, October 9, 2009 - 3:41:08 PM
Last modification on : Thursday, August 4, 2022 - 5:05:39 PM

Identifiers

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

Citation

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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