Skip to Main content Skip to Navigation
Reports

Dynamics and bifurcations of the adaptive exponential integrate-and-fire model

Jonathan Touboul 1, 2, * Romain Brette 1
* Corresponding author
1 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 : Recently, several two-dimensional spiking neuron models have been introduced, with the aim of reproducing the diversity of electrophysiological features displayed by real neurons while keeping a simple model, for simulation and analysis purposes. Among these models, the adaptive integrate-and-fire model is physiologically relevant in that its parameters can be easily related to physiological quantities. The interaction of the differential equations with the reset results in a rich and complex dynamical structure. We relate the subthreshold features of the model to the dynamical properties of the differential system and the spike patterns to the properties of a Poincaré map defined by the sequence of spikes. We find a complex bifurcation structure which has a direct interpretation in terms of spike trains. For some parameter values, spike patterns are chaotic.
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download

https://hal.inria.fr/inria-00288734
Contributor : Jonathan Touboul <>
Submitted on : Wednesday, July 2, 2008 - 5:00:46 PM
Last modification on : Tuesday, September 22, 2020 - 3:58:11 AM
Long-term archiving on: : Friday, September 24, 2010 - 10:41:43 AM

File

RRTouboulBrette.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00288734, version 4

Collections

Citation

Jonathan Touboul, Romain Brette. Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. [Research Report] RR-6563, INRIA. 2008. ⟨inria-00288734v4⟩

Share

Metrics

Record views

636

Files downloads

1069