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} }