Abstract
Though much work has been devoted to the analysis of synchronization, the synchronization paths and the underlying mechanism between community structure and synchronization are far from understood. This paper focuses on the cooperation of local and collective synchronization to understand the synchronization paths in complex networks, where the local and collective synchronization describe the states of nodes in the same community and across different communities respectively. By analyzing the eigenvalues of the networks, we find that when the community structure is weak, a tradeoff exists between local-synchronization (synchronization in the same community) and across-synchronization (synchronization across different communities), which guarantees the stability of the collective synchronization, yet with different synchronization paths. However, when the strength of community structure is strong, collective synchronization is mainly determined by the across-synchronization.
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