Phase chaos in the dynamics of an ensemble of oscillators with time-modulated global coupling

The object of consideration is an ensemble of globally coupled self-sustained oscillating elements with a finite-width frequency distribution. The ensemble interacts with the field of a resonator, which is a linear oscillator with a frequency doubly exceeding the mean frequency of the oscillators in the ensemble. The global coupling is switched on and off alternately, so that the ensemble alternatively passes from synchrony to asynchrony (Kuramoto transition). At each stage of activity (synchronization), the field of the resonator causes the mean field of the ensemble to oscillate so that the phase doubles compared with the previous stage of excitation. Therefore, the mean field dynamics is chaotic and, as follows from numerical simulation data, can be associated with the Smale–Williams attractor. Systems of this type can be applied in electronics, specifically, in secure communication systems, noise location, etc.