Analysis of cluster explosive synchronization in complex networks

Correlations between intrinsic dynamics and local topology have become a new trend in the study of synchronization in complex networks. In this paper, we investigate in this paradigm the influence of topology on dynamics of networks made up of second-order Kuramoto oscillators. In particular, based on mean-field calculations, we provide a detailed investigation of the recently reported phenomena of cluster explosive synchronization (CES)[Phys. Rev. Lett. 110, 218701 (2013)], analysing the model in scale-free and small-world networks as a function of several topological properties. We show that, in contrast to scale-free networks, the transition to the synchronous state in small-world structures tends to be continuous as the probability of rewiring increases. These results complement the previous findings regarding CES and also fundamentally deepen the understanding of the interplay between topology and dynamics under the constraint of correlating natural frequencies and local structure.