In this paper, we study chaos synchronization in complex networks with time-invariant, time-varying and switching configurations based on the matrix measure of complex matrices. To begin with, we propose an analytical condition for chaos synchronization in complex networks with a time-invariant configuration. Secondly, we obtain some less conservative synchronization conditions for networks with a time-varying configuration. Thirdly, we consider chaos synchronization in networks with time-average and switching configurations. If complex subnetworks satisfy certain conditions, the networks with time-average and switching configurations are M-synchronizable. At last, we analyze the nonsynchronizability of complex networks. Chaos synchronization in complex networks can't be realized if the coupling configuration and the inner-coupling matrix satisfy certain conditions. Theoretical analysis and numerical simulations verify the effectiveness of the proposed synchronization criteria.
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Maoyin Chen (2008) studied this question.
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