The Cacophony of Interconnected Networks

Abstract

The harmony of an orchestra emerges from the individual effort of musicians towards mutual synchronization of their tempi. When the orchestra is split between two concert halls communicating via Internet, a time delay is imposed which might hinder synchronization. We present this type of system as two interconnected networks of oscillators with a time delay and analyze its dynamics as a function of the couplings and communication lag. We describe a breathing synchronization regime, namely, for a wide range of parameters, two groups emerge in the orchestra within the same concert hall playing at different tempi. Each group has a mirror in the other hall, one group is in phase and the other in anti-phase with their mirrors. For strong couplings, a phase shift between halls might occur. The implications of our findings on other interconnected systems are also discussed.