title: Dynamics and bifurcations of the adaptive exponential integrate-and-fire model.
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.
authors.affiliation: Département d'Informatique, Projet Odyssée, Ecole Normale Supérieure, 45, rue d'Ulm, 75230, Paris Cedex 05, France.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Touboul
authors.forename: Romain
authors.initials: R
authors.lastname: Brette
mesh_terms: D000200:Action Potentials / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*