Delay regulated explosive synchronization in multiplex networks

Abstract

It is known that explosive synchronization (ES) in an isolated network of Kuramoto oscillators with inertia is significantly enhanced by the presence of time delay. Here we show that time delay in one layer of the multiplex network governs the transition to synchronization and ES in the other layers. We found that a single layer with time-delayed intra-layer coupling may experience a different type of transition to synchronization, e.g. ES or continuous, depending on the values of time delay. Importantly, the same type of transition is incorporated simultaneously in other layer(s) as well, irrespective of the intra-layer delay values. Hence, a suitable choice of time-delay in only one layer of a multiplex network can lead to a desired (either ES or continuous) transition simultaneously in the other layers, either directly or remotely connected to the delayed layer. These results offer a platform for a better understanding of the dynamics of those complex systems which are represented by the multilayered framework and contain time delays in the communication processes.