The Cacophony of Interconnected Networks

Abstract The harmony of an orchestra emerges from the individual effort of musi-cians towards mutual synchronization of their tempi. When the orchestra is split be-tween 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. Technology has furnished us with global connectivity changing the functioning of cooperative work, international business, and interpersonal relationships. Today, it is possible to distribute an orchestra over two concert halls in different conti-nents. Fast Internet connections would provide the communication infrastructure to properly combine the sounds [12]. As there is always a physical limit speed to infor-mation transport, the communication between sub-orchestras is subjected to a time delay due to the distance between halls. As we discuss here, this time delay might pose a real challenge to the synchronizability among musicians, which is vital t