by Romain Brette
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.
Reference:
Romain Brette, 2008. The Cauchy problem for one-dimensional spiking neuron models, Cognitive neurodynamics, volume 2.
Bibtex Entry:
@article{Brette2008,
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.},
author = {Brette, Romain},
day = {15},
doi = {10.1007/s11571-007-9032-y},
issn = {1871-4080},
journal = {Cognitive neurodynamics},
language = {eng},
month = {Mar},
number = {1},
pages = {21--27},
title = {The Cauchy problem for one-dimensional spiking neuron models.},
url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2289251/pdf/11571_2007_Article_9032.pdf},
volume = {2},
year = {2008}
}