KINETIC THEORY FOR NEURONAL NETWORK DYNAMICS*

Document Type

Article

Publication Date

1-1-2006

Abstract

We present a detailed theoretical framework for statistical descriptions of neuronal networks and derive (1 + 1)-dimensional kinetic equations, without introducing any new parameters, directly from conductance-based integrate-and-fire neuronal networks. We describe the details of derivation of our kinetic equation, proceeding from the simplest case of one excitatory neuron, to coupled networks of purely excitatory neurons, to coupled networks consisting of both excitatory and inhibitory neurons. The dimension reduction in our theory is achieved via novel moment closures. We also describe the limiting forms of our kinetic theory in various limits, such as the limit of mean-driven dynamics and the limit of infinitely fast conductances. We establish accuracy of our kinetic theory by comparing its prediction with the full simulations of the original point-neuron networks. We emphasize that our kinetic theory is dynamically accurate, i.e., it captures very well the instantaneous statistical properties of neuronal networks under time-inhomogeneous inputs.

Identifier

33845421047 (Scopus)

Publication Title

Communications in Mathematical Sciences

External Full Text Location

https://doi.org/10.4310/CMS.2006.v4.n1.a4

e-ISSN

19450796

ISSN

15396746

First Page

97

Last Page

127

Issue

1

Volume

4

Grant

DMS-0211655

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS