A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics
| dc.creator | Cessac, B. | |
| dc.date | 2007-06-01 | |
| dc.date.accessioned | 2026-07-07T09:19:41Z | |
| dc.date.available | 2026-07-07T09:19:41Z | |
| dc.description | 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. | |
| dc.description | 56 pages, 1 Figure, to appear in Journal of Mathematical Biology | |
| dc.identifier | https://arxiv.org/abs/0706.0077 | |
| dc.identifier | http://arxiv.org/abs/0706.0077 | |
| dc.identifier | Journal of Mathematical Biology, Volume 56, Number 3, 311-345 (2008). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154484 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Neurons and Cognition | |
| dc.title | A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics | |
| dc.type | text |