  Macroscopic oscillations in the brain are involved in various cognitive and
physiological processes, yet their precise function is not not completely
understood. Communication Through Coherence (CTC) theory proposes that these
rhythmic electrical patterns might serve to regulate the information flow
between neural populations. Thus, to communicate effectively, neural
populations must synchronize their oscillatory activity, ensuring that input
volleys from the presynaptic population reach the postsynaptic one at its
maximum phase of excitability. We consider an Excitatory-Inhibitory (E-I)
network whose macroscopic activity is described by an exact mean-field model.
The E-I network receives periodic inputs from either one or two external
sources, for which effective communication will not be achieved in the absence
of control. We explore strategies based on optimal control theory for
phase-amplitude dynamics to design a control that sets the target population in
the optimal phase to synchronize its activity with a specific presynaptic input
signal and establish communication. The control mechanism resembles the role of
a higher cortical area in the context of selective attention. To design the
control, we use the phase-amplitude reduction of a limit cycle and leverage
recent developments in this field in order to find the most effective control
strategy regarding a defined cost function. Furthermore, we present results
that guarantee the local controllability of the system close to the limit
cycle.
