title: Statistical physics approaches to neuronal network dynamics.
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.
authors: Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China. cai@cims.nyu.edu
authors: David
authors: D
authors: Cai
authors: Louis
authors: L
authors: Tao
mesh_terms: D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009010:Monte Carlo Method; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*