Explosive synchronization in complex networks

Synchronization in coupled oscillators is one of the most important filed in statistical physics and complex systems. In the past a few decades, it is shown that most synchronization transitions are continuous (second-order), i.e., the order parameter increases continuously after the transition point. However, recently it has been revealed that in certain systems of coupled oscillators, synchronization could be explosive (first-order), where the order parameter suddenly jumps after the transition and a hysteresis loop exists due to the irreversibility between the forward and backward transitions. These findings have opened a new area since the explosive synchronization is essentially different from the continuous one. In this paper, we review the important advances so far in this direction, including the explosive synchronization in coupled oscillators with degree-frequency correlation, the explosive synchronization in frequency-weighted Kuramoto model, the explosive synchronization in coupled conformists and contrarians, the explosive synchronization in adaptive and multilayer networks, as well as the microscopic mechanism of the explosive synchronization and the experimental verification. These work not only have greatly enhanced our understandings of synchronization in complex systems and promoted the development of synchronization theory, but also paved a way for potential applications in future.