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Effects of the Frequency-degree Correlation on Local Synchronization in Complex Networks
Shijin Jiang,Wenyi Fang,Shaoting Tang,Sen Pei,Shu Yan,Zhiming Zheng 한국물리학회 2015 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.67 No.2
We investigate the effects of the frequency-degree correlation on local synchronization in complex networks with Kuramoto oscillators. We find that a discontinuous synchronization transition occurs in the local patterns for heterogenous networks while for homogenous networks, the local synchronization transition remains continuous. Then, we extend our study to a general frequency-degree correlation case and conclude that the positive correlation does not change the local synchronization patterns while in the case of a negative correlation, the local synchronization transition degenerates to second order. Moreover, the correlation parameter α is verified to have a strong influence on the synchronization level. In particular, smaller |α| results in higher synchronization ability and faster speed to a synchronized state. Our study provides a deeper understanding of the effects of the frequency-degree correlation on network synchronization.