  Spontaneous explosive emergent behavior takes place in heterogeneous networks
when the frequencies of the nodes are positively correlated to the node degree.
A central feature of such explosive transitions is a hysteretic behavior at the
transition to synchronization. We unravel the underlying mechanisms and show
that the dynamical origin of the hysteresis is a change of basin of attraction
of the synchronization state. Our findings hold for heterogeneous networks with
star graph motifs such as scale free networks, and hence reveal how microscopic
network parameters such as node degree and frequency affect the global network
properties and can be used for network design and control.
