Synchronization in Multilayer Networks: When Good Links Go Bad

Abstract

Many complex biological and technological systems can be represented by multilayer networks where the nodes are coupled via several independent networks. Despite its significance from both the theoretical and the application perspectives, synchronization in multilayer networks and its dependence on the network topology remain poorly understood. In this paper, we develop a universal connection graph-based method which opens up the possibility of explicitly assessing critical multilayer-induced interactions which can hamper network synchronization. The method reveals striking, counterintuitive effects caused by multilayer coupling. It demonstrates that a coupling which is favorable to synchronization in single-layer networks can reverse its role and destabilize synchronization when used in a multilayer network. This property is controlled by the traffic load on a given edge when the replacement of a lightly loaded edge in one layer with a coupling from another layer can promote synchronization, but a similar replacement of a highly loaded edge can break synchronization, forcing a “good” link to go “bad.” This method can be transformative in the highly active research field of synchronization in multilayer engineering and social networks, especially in regard to hidden effects not seen in single-layer networks.