中国物理B ›› 2009, Vol. 18 ›› Issue (6): 2209-2212.doi: 10.1088/1674-1056/18/6/017

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Synchronization speed of identical oscillators on community networks

张智, 傅忠谦, 严钢   

  1. Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2008-09-16 修回日期:2008-10-06 出版日期:2009-06-20 发布日期:2009-06-20

Synchronization speed of identical oscillators on community networks

Zhang Zhi(张智), Fu Zhong-Qian(傅忠谦)†, and Yan Gang(严钢)   

  1. Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230026, China
  • Received:2008-09-16 Revised:2008-10-06 Online:2009-06-20 Published:2009-06-20

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摘要： Synchronizability of complex oscillators networks has attracted much research interest in recent years. In contrast, in this paper we investigate numerically the synchronization speed, rather than the synchronizability or synchronization stability, of identical oscillators on complex networks with communities. A new weighted community network model is employed here, in which the community strength could be tunable by one parameter δ. The results showed that the synchronization speed of identical oscillators on community networks could reach a maximal value when δ is around 0.1. We argue that this is induced by the competition between the community partition and the scale-free property of the networks. Moreover, we have given the corresponding analysis through the second least eigenvalue λ2 of the Laplacian matrix of the network which supports the previous result that the synchronization speed is determined by the value of λ2.

关键词: complex networks, synchronization speed, community

Abstract: Synchronizability of complex oscillators networks has attracted much research interest in recent years. In contrast, in this paper we investigate numerically the synchronization speed, rather than the synchronizability or synchronization stability, of identical oscillators on complex networks with communities. A new weighted community network model is employed here, in which the community strength could be tunable by one parameter $\delta$. The results showed that the synchronization speed of identical oscillators on community networks could reach a maximal value when $\delta$ is around 0.1. We argue that this is induced by the competition between the community partition and the scale-free property of the networks. Moreover, we have given the corresponding analysis through the second least eigenvalue $\lambda_2$ of the Laplacian matrix of the network which supports the previous result that the synchronization speed is determined by the value of $\lambda_2$.

Key words: complex networks, synchronization speed, community

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
05.45.Xt (Synchronization; coupled oscillators)