  The theory of communication through coherence (CTC) proposes that brain
oscillations reflect changes in the excitability of neurons, and therefore the
successful communication between two oscillating neural populations depends not
only on the strength of the signal emitted but also on the relative phases
between them. More precisely, effective communication occurs when the emitting
and receiving populations are properly phase locked so the inputs sent by the
emitting population arrive at the phases of maximal excitability of the
receiving population. To study this setting, we consider a population rate
model consisting of excitatory and inhibitory cells modelling the receiving
population, and we perturb it with a time-dependent periodic function modelling
the input from the emitting population. We consider the stroboscopic map for
this system and compute numerically the fixed and periodic points of this map
and their bifurcations as the amplitude and the frequency of the perturbation
are varied. From the bifurcation diagram, we identify the phase-locked states
as well as different regions of bistability. We explore carefully the dynamics
emphasizing its implications for the CTC theory. In particular, we study how
the input gain depends on the timing between the input and the inhibitory
action of the receiving population. Our results show that naturally an optimal
phase locking for CTC emerges, and provide a mechanism by which the receiving
population can implement selective communication. Moreover, the presence of
bistable regions, suggests a mechanism by which different communication regimes
between brain areas can be established without changing the structure of the
network
