2003/02/28 by Hideo Hasegawa · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · Physics and Astronomy · #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.68.041909
published as Phys. Rev. E 68 (2003) 041909 · 21 pages, 3 figures, revised the text
arxiv created 2003/04/11 · openalex publication_date 2003/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E 67, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of N-unit neurons, each of which is expressed by coupled K-dimensional differential equations (DEs), are assumed to be subject to spatially correlated white noises. The original KN-dimensional stochastic DEs have been replaced by K(K+2)-dimensional deterministic DEs expressed in terms of means and the second-order moments of local and global variables: the fourth-order contributions are taken into account by the Gaussian decoupling approximation. Our DMA has been applied to an ensemble of Hodgkin-Huxley (HH) neurons (K=4), for which effects of the noise, the coupling strength, and the ensemble size on the response to a single-spike input have been investigated. Numerical results calculated by the DMA theory are in good agreement with those obtained by direct simulations, although the former computation is about a thousand times faster than the latter for a typical HH neuron ensemble with N=100.