Explosive Synchronization In Complex Network

Explosive synchronization means that transition from incoherence to synchro-nization is first-order like, discontinuous and irreversible. It’s very different from the traditional continuous second-order synchronization transition. This phenomenon shows similar characteristics with abrupt transition phenomenon in real world, such as epileptic seizure in brain and cascading failure in power grid. As explosive per-colation is very hot in complex network science, since its finding in 2011, explosive synchronization has become a very new hot topic. The first work on this topic shows that two conditions are necessary for explosive synchronization to show up:a scale-free network topology and the correlation between natural frequencies and degrees of the nodes, thus the condition for explosive synchronization was very strict. In order to understand this phenomenon better, we study the mechanism of explosive synchro-nization by both numerical simulation and theoretical analysis. Our works go through many aspects of explosive synchronization. The main results are concluded as follow-ing:1、We introduce a frequency weighted model and study explosive synchroniza-tion in a general network with a general frequency distribution.2、We study the correlation between oscillators in network and find the "suppres-sive rule" could be the reason of explosive synchronization. We argue that explosive synchronization can be regarded as a process of explosive percolation in dynamical space.3、Taking advantage of suppressive rule, we introduce a local order parameter weighed Kuramoto model and find explosive synchronization can occur in the multi-layer and adaptive networks.4、We study Chimera state with an explosive synchronization model and argue that bistability could be the natural link between these two important phenomena.5、We find "contrarians" can change synchronization transition from discontin-uous to continuous, which could be a good way to suppress explosive synchronization in network.