Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises.

A semianalytical dynamical mean-field theory has been developed for a study of dynamics of an ensemble of N-unit FitzHugh-Nagumo neurons subject to white noises. Assuming weak noises and the Gaussian distribution of state variables, we have driven equations of motions for moments of local and global variables. Dynamical mean-field approximation (DMA) has replaced original, 2N-dimensional stochastic differential equations (DEs) by eight-dimensional deterministic DEs, whereas the conventional moment method yields N(2N+3)-dimensional deterministic DEs for local variables. We have discussed the dependence of the spike firing precision and the synchronization on the noise intensity, synaptic coupling, and the size of the neuron ensemble. The spike timing precision is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. Results calculated by our DMA theory are in good agreement with those obtained by direct simulations. DMA theory is extended to a large cluster which can be divided into multiple subclusters according to their functions. A model calculation has demonstrated that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy subclusters with feed-forward couplings, as in the synfire chain. We have compared DMA theory with the conventional moment method, showing that the former may be alternatively derived from the latter by a reduction in the number of moments with the mean-field approximation.