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Updated: Jun 28, 2026

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
Published on: June 21, 2022
The Cauchy problem for one-dimensional spiking neuron models
1Equipe Odyssée (INRIA/ENS/ENPC), Département d'Informatique, Ecole Normale Supérieure, 45, Rue D'Ulm, 75230, Paris Cedex 05, France, brette@di.ens.fr.
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.
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