title: The Cauchy problem for one-dimensional spiking neuron models.
abstract: I consider spiking neuron models defined by a one-dimensional differential equation and a reset-i.e., neuron models of the integrate-and-fire type. I address the question of the existence and uniqueness of a solution on [Formula: see text] for a given initial condition. It turns out that the reset introduces a countable and ordered set of backward solutions for a given initial condition. I discuss the implications of these mathematical results in terms of neural coding and spike timing precision.
authors.affiliation: Equipe Odyssée (INRIA/ENS/ENPC), Département d'Informatique, Ecole Normale Supérieure, 45, Rue D'Ulm, 75230, Paris Cedex 05, France, brette@di.ens.fr.
authors.forename: Romain
authors.initials: R
authors.lastname: Brette