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:10.1162/089976600300015493

Markdown

[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:10.1162/089976600300015493

BibTeX

@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/}
}