Abstract:
This talk relays the results of

N Brunel (2000), Dynamics of sparsely connected networks of excitatory
and inhibitory spiking neurons, J. Comp. Neurosci., 8:183-208.

The author describes a leaky integrate and fire network of excitatory
and inhibitory neurons and building on earlier work uses mean-field
methods to analyze its behavior when the network size is large and
connectivity is sparse.  Stationary states and Hopf-bifurcations in
the mean-field approximation are analyzed.  Approximations of
interspike-time distribution statistics (e.g., firing rate, coefficient
of variation) are derived for some stationary states, in addition to
frequency of oscillations near Hopf bifurcations.  The authors include
comparisons with numerical simulations, which will also be discussed
in the talk.