  We study some mechanisms responsible for synchronous oscillations and loss of
synchrony at physiologically relevant frequencies (10-200 Hz) in a network of
heterogeneous inhibitory neurons. We focus on the factors that determine the
level of synchrony and frequency of the network response, as well as the
effects of mild heterogeneity on network dynamics. With mild heterogeneity,
synchrony is never perfect and is relatively fragile. In addition, the effects
of inhibition are more complex in mildly heterogeneous networks than in
homogeneous ones. In the former, synchrony is broken in two distinct ways,
depending on the ratio of the synaptic decay time to the period of repetitive
action potentials ($\tau_s/T$), where $T$ can be determined either from the
network or from a single, self-inhibiting neuron. With $\tau_s/T > 2$,
corresponding to large applied current, small synaptic strength or large
synaptic decay time, the effects of inhibition are largely tonic and
heterogeneous neurons spike relatively independently. With $\tau_s/T < 1$,
synchrony breaks when faster cells begin to suppress their less excitable
neighbors; cells that fire remain nearly synchronous. We show numerically that
the behavior of mildly heterogeneous networks can be related to the behavior of
single, self-inhibiting cells, which can be studied analytically.
