  Explosive synchronization (ES) is nowadays a hot topic of interest in
nonlinear science and complex networks. So far, it is conjectured that ES is
rooted in the setting of specific microscopic correlation features between the
natural frequencies of the networked oscillators and their effective coupling
strengths. We show that ES, in fact, is far more general, and can occur in
adaptive and multilayer networks also in the absence of such correlation
properties. Precisely, we first report evidence of ES in the absence of
correlation for networks where a fraction f of the nodes have links adaptively
controlled by a local order parameter, and then we extend the study to a
variety of two-layer networks with a fraction f of their nodes coupled each
other by means of dependency links. In this latter case, we even show that ES
sets in, regardless of the differences in the frequency distribution and/or in
the topology of connections between the two layers. Finally, we provide a
rigorous, analytical, treatment to properly ground all the observed scenario,
and to facilitate the understanding of the actual mechanisms at the basis of ES
in real-world systems.
