  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.
