A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics
Dynamical Systems
2008-02-12 v1 Chaotic Dynamics
Neurons and Cognition
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.
Keywords
Cite
@article{arxiv.0706.0077,
title = {A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics},
author = {B. Cessac},
journal= {arXiv preprint arXiv:0706.0077},
year = {2008}
}
Comments
56 pages, 1 Figure, to appear in Journal of Mathematical Biology