Synchronization speed of identical oscillators on community networks

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 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 $\lambda_2$.