Synchronization speed of identical oscillators on community networks

Synchronizability of complex oscillators networks has attracted muchresearch interest in recent years. In contrast, in this paper weinvestigate numerically the synchronization speed, rather than thesynchronizability or synchronization stability, of identicaloscillators on complex networks with communities. A new weightedcommunity network model is employed here, in which the communitystrength could be tunable by one parameter $delta$. The resultsshowed that the synchronization speed of identical oscillators oncommunity networks could reach a maximal value when $delta$ isaround Synchronizability of complex oscillators networks has attracted muchresearch interest in recent years. In contrast, in this paper weinvestigate numerically the synchronization speed, rather than thesynchronizability or synchronization stability, of identicaloscillators on complex networks with communities. A new weightedcommunity network model is employed here, in which the communitystrength could be tunable by one parameter $delta$. The resultsshowed that the synchronization speed of identical oscillators oncommunity networks could reach a maximal value when $delta$ isaround $0.1$. We argue that this is induced by the competitionbetween the community partition and the scale-free property of thenetworks. Moreover, we have given the corresponding analysis throughthe second least eigenvalue $lambda_2$ of the Laplacian matrix ofthe network which supports the previous result that thesynchronization speed is determined by the value of $lambda_2$.