Effects of Reduced Frequency on Network Configuration and Synchronization Transition

Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of 'reduced frequency', a measure which can quantify natural frequencies of each pair of oscillators. Then we introduce an evolving network whose linking rules are controlled by its own dynamical property. The simulation results indicate that when the linking probability positively correlates with the reduced frequency, the network undergoes a first-order phase transition. Meanwhile, we discuss the circumstance under which an explosive synchronization can be ignited. The numerical results show that the peculiar butterfly shape correlation between frequencies and degrees of the nodes contributes to an explosive synchronization transition.