Edges of inter-layer synchronization in multilayer networks with time-switching links

TL;DR

This paper studies how the synchronization transition in multilayer networks is affected by time-switching inter-layer links, revealing smooth and abrupt transitions depending on the switching time and connectivity.

Contribution

It introduces the analysis of synchronization in multilayer networks with dynamic inter-layer links and identifies conditions for abrupt transitions.

Findings

Smooth transition to synchronization with static links

Enhanced synchronizability with dynamic switching

Abrupt transition at critical switching times

Abstract

We investigate the transition to synchronization in a two-layer network with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the time-scale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical units in the layers, we observe a significant improvement in the system synchronizability, i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching-time, the transition to synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as the shrinking, and ultimately, the disappearance of the basin of attraction of a desynchronized network state.