  Recent experiments suggest that inhibitory networks of interneurons can
synchronize the neuronal discharge in in vitro hippocampal slices. Subsequent
theoretical work has shown that strong synchronization by mutual inhibition is
only moderately robust against neuronal heterogeneities in the current drive,
provided by activation of metabotropic glutamate receptors. In vivo neurons
display greater variability in the interspike intervals due to the presence of
synaptic noise. Noise and heterogeneity affect synchronization properties
differently. In this paper we study using model simulations how robust
synchronization can be in the presence of synaptic noise and neuronal
heterogeneity. We find that with at least a minimum amount of noise stochastic
weak synchronization (SWS) (i.e. when neurons spike within a short interval
from each other, but not necessarily at each period) is produced that is much
more robust than strong synchronization (i.e. when neurons spike each period).
The statistics of the SWS population discharge are consistent with previous
experimental data. We find robust SWS in the gamma frequency range (20-80 Hz)
for a stronger synaptic coupling compared to previous models and for networks
with 10 -- 1000 neurons.
