A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E { \bf 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 The original $KN$-dimensional { \it stochastic} DEs have been replaced by $K(K+2)$-dimensional { \it deterministic} DEs expressed in terms of means and the second-order moments of { \it local} and { \it global} variables: the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. Results calculated by DMA theory are in good agreement with those obtained by direct simulations.
Categories: cond-mat.dis-nn q-bio.NC