Double explosive transition in the synchronization of multilayer networks

We give evidence that consecutive explosive transitions may occur in two-layered networks, when a dynamical layer made of an ensemble of networking phase oscillators interacts with an environmental layer of oscillators which are in a state of approximate synchronization. Under these conditions, the interlayer coupling induces two consecutive explosive transitions in the dynamical layer, each one associated with a hysteresis loop. We also show that the same phenomenon can be observed when the environmental layer is simplified into a single node with phase lag. Theoretical arguments unveil that the mechanisms at the basis of the two transitions are in fact different, with the former originating from a coupling-amplified disorder and the latter originating from a coupling-induced synchronization. We discuss the relevance of the observed state in brain dynamics and show how it may emerge in a real brain network.