Controlling synchrony in oscillatory networks with a separate stimulation-registration setup

We present a demand-controlled method for desynchronization of globally coupled oscillatory networks utilizing a configuration with an observed and stimulated subsystem. The stimulated subsystem is subjected to a proportional-integro-differential (PID) feedback derived from the mean field of the observed subsystem. Our method enables to restore desynchronized states in both subsystems in a robust way. We develop an analytical theory for the Kuramoto model and analytically derive a threshold of the stimulation parameters for the desynchronization transition in ensembles of phase and van der Pol oscillators. We also numerically demonstrate the efficacy of the approach for ensembles of globally coupled Landau-Stuart and relaxation van der Pol oscillators. Our approach is particularly important for applications to physical and biological systems which do not allow for a simultaneous registration and stimulation of the whole network, as in the case of electrical brain stimulation.