  Oscillations are a hallmark of neural population activity in various brain
regions with a spectrum covering a wide range of frequencies. Within this
spectrum gamma oscillations have received particular attention due to their
ubiquitous nature and to their correlation with higher brain functions.
Recently, it has been reported that gamma oscillations in the hippocampus of
behaving rodents are segregated in two distinct frequency bands: slow and fast.
These two gamma rhythms correspond to dfferent states of the network, but their
origin has been not yet clarified. Here, we show theoretically and numerically
that a single inhibitory population can give rise to coexisting slow and fast
gamma rhythms corresponding to collective oscillations of a balanced spiking
network. The slow and fast gamma rhythms are generated via two different
mechanisms: the fast one being driven by the coordinated tonic neural firing
and the slow one by endogenous fluctuations due to irregular neural activity.
We show that almost instantaneous stimulations can switch the collective gamma
oscillations from slow to fast and vice versa. Furthermore, to make a closer
contact with the experimental observations, we consider the modulation of the
gamma rhythms induced by a slower (theta) rhythm driving the network dynamics.
In this context, depending on the strength of the forcing, we observe
phase-amplitude and phase-phase coupling between the fast and slow gamma
oscillations and the theta forcing. Phase-phase coupling reveals different
theta-phases preferences for the two coexisting gamma rhythms.
