Reduction of Conductance-Based Models with Slow Synapses to Neural Nets
Abstract
The method of averaging and a detailed bifurcation calculation are used to reduce a system of synaptically coupled neurons to a Hopfield type continuous time neural network. Due to some special properties of the bifurcation, explicit averaging is not required and the reduction becomes a simple algebraic problem. The resultant calculations show one how to derive a new type of “squashing function” whose properties are directly related to the detailed ionic mechanisms of the membrane. Frequency encoding as opposed to amplitude encoding emerges in a natural fashion from the theory. The full system and the reduced system are numerically compared.
Cite
Text
Ermentrout. "Reduction of Conductance-Based Models with Slow Synapses to Neural Nets." Neural Computation, 1994. doi:10.1162/NECO.1994.6.4.679Markdown
[Ermentrout. "Reduction of Conductance-Based Models with Slow Synapses to Neural Nets." Neural Computation, 1994.](https://mlanthology.org/neco/1994/ermentrout1994neco-reduction/) doi:10.1162/NECO.1994.6.4.679BibTeX
@article{ermentrout1994neco-reduction,
title = {{Reduction of Conductance-Based Models with Slow Synapses to Neural Nets}},
author = {Ermentrout, Bard},
journal = {Neural Computation},
year = {1994},
pages = {679-695},
doi = {10.1162/NECO.1994.6.4.679},
volume = {6},
url = {https://mlanthology.org/neco/1994/ermentrout1994neco-reduction/}
}