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Journal Articles Journal of Mathematical Biology Year : 2008

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

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.

Dates and versions

inria-00423350 , version 1 (09-10-2009)

Identifiers

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

Cite

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