Explosive synchronization in a general complex network

Explosive synchronization (ES) has recently attracted much attention, where its two necessary conditions are found to be a scale-free network topology and a positive correlation between the natural frequencies of the oscillators and their degrees. Here we present a framework for ES to be observed in a general complex network, where a positive correlation between coupling strengths of the oscillators and the absolute of their natural frequencies is assumed and the previous studies are included as specific cases. In the framework, the previous two necessary conditions are replaced by another one, thus fundamentally deepening the understanding of the microscopic mechanism toward synchronization. A rigorous analytical treatment by a mean field is provided to explain the mechanism of ES in this alternate framework.