  We have proposed a generalized Langevin-type rate-code model subjected to
multiplicative noise, in order to study stationary and dynamical properties of
an ensemble containing {\it finite} $N$ neurons. Calculations using the
Fokker-Planck equation (FPE) have shown that owing to the multiplicative noise,
our rate model yields various kinds of stationary non-Gaussian distributions
such as gamma, inverse-Gaussian-like and log-normal-like distributions, which
have been experimentally observed. Dynamical properties of the rate model have
been studied with the use of the augmented moment method (AMM), which was
previously proposed by the author with a macroscopic point of view for
finite-unit stochastic systems. In the AMM, original $N$-dimensional stochastic
differential equations (DEs) are transformed into three-dimensional
deterministic DEs for means and fluctuations of local and global variables.
Dynamical responses of the neuron ensemble to pulse and sinusoidal inputs
calculated by the AMM are in good agreement with those obtained by direct
simulation. The synchronization in the neuronal ensemble is discussed.
Variabilities of the firing rate and of the interspike interval (ISI) are shown
to increase with increasing the magnitude of multiplicative noise, which may be
a conceivable origin of the observed large variability in cortical neurons.
