  Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings
subject to white noises, has been studied by using both direct simulations and
a semi-analytical augmented moment method (AMM) which has been proposed in a
recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For $N$-unit FN neuron
ensembles, AMM transforms original $2N$-dimensional {\it stochastic} delay
differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs
for means and correlation functions of local and global variables.
Infinite-order recursive DEs are terminated at the finite level $m$ in the
level-$m$ AMM (AMM$m$), yielding $8(m+1)$-dimensional deterministic DEs. When a
single spike is applied, the oscillation may be induced if parameters of
coupling strength, delay, noise intensity and/or ensemble size are appropriate.
Effects of these parameters on the emergence of the oscillation and on the
synchronization in FN neuron ensembles have been studied. The synchronization
shows the {\it fluctuation-induced} enhancement at the transition between
non-oscillating and oscillating states. Results calculated by AMM5 are in
fairly good agreement with those obtained by direct simulations.
