  Collective oscillations and their suppression by external stimulation are
analyzed in a large-scale neural network consisting of two interacting
populations of excitatory and inhibitory quadratic integrate-and-fire neurons.
In the limit of an infinite number of neurons, the microscopic model of this
network can be reduced to an exact low-dimensional system of mean-field
equations. Bifurcation analysis of these equations reveals three different
dynamic modes in a free network: a stable resting state, a stable limit cycle,
and bistability with a coexisting resting state and a limit cycle. We show that
in the limit cycle mode, high-frequency stimulation of an inhibitory population
can stabilize an unstable resting state and effectively suppress collective
oscillations. We also show that in the bistable mode, the dynamics of the
network can be switched from a stable limit cycle to a stable resting state by
applying an inhibitory pulse to the excitatory population. The results obtained
from the mean-field equations are confirmed by numerical simulation of the
microscopic model.
