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Statistical physics approaches to neuronal network dynamics

CAI David^*, TAO Louis

Institute of Natural Sciences and Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China； 2Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, NY 10012, USA

Abstract

We review a statistical physics approach for reduced descriptions of neuronal network dynamics. From a network of all-to-all coupled, excitatory integrate-and-fire neurons, we derive a (2+1)-D advection-diffusion equation for a probability distribution function, which describes neuronal population dynamics. We further show how to derive a (1+1)-D kinetic equation, using a moment closure scheme, without introducing any new parameters to the system. We demonstrate the numerical accuracy of our kinetic theory by comparing its results to Monte Carlo simulations of the full integrate-and-fire neuronal network.

Key words: neuronal networks; coarse-graining; fluctuations; diffusion; neuronal population

Received: 　　Accepted:

Corresponding author: 蔡申瓯　　E-mail: cai@cims.nyu.edu

Citing This Article：

CAI David, TAO Louis . Statistical physics approaches to neuronal network dynamics. Acta Physiol Sin 2011; 63 (5): 453-462 (in Chinese with English abstract).