The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result
Abstract
The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.
Cite
Text
Knight et al. "The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result." Neural Computation, 2000. doi:10.1162/089976600300015493Markdown
[Knight et al. "The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result." Neural Computation, 2000.](https://mlanthology.org/neco/2000/knight2000neco-approach/) doi:10.1162/089976600300015493BibTeX
@article{knight2000neco-approach,
title = {{The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result}},
author = {Knight, Bruce W. and Omurtag, Ahmet and Sirovich, L.},
journal = {Neural Computation},
year = {2000},
pages = {1045-1055},
doi = {10.1162/089976600300015493},
volume = {12},
url = {https://mlanthology.org/neco/2000/knight2000neco-approach/}
}