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

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