Feedback suppression of neural synchrony in two interacting populations by vanishing stimulation

We discuss the suppression of collective synchrony in a system of two interacting oscillatory networks. It is assumed that the first network can be affected by the stimulation, whereas the activity of the second one can be monitored. The study is motivated by ongoing attempts to develop efficient techniques for the manipulation of pathological brain rhythms. The suppression mechanism we consider is related to the classical problem of interaction of active and passive systems. The main idea is to connect a specially designed linear oscillator to the active system to be controlled. We demonstrate that the feedback loop, organized in this way, provides an efficient suppression. We support the discussion of our approach by a theoretical treatment of model equations for the collective modes of both networks, as well as by the numerical simulation of two coupled populations of neurons. The main advantage of our approach is that it provides a vanishing-stimulation control, i.e., the stimulation reduces to the noise level as soon as the goal is achieved.