Partial Synchronizability Characterized by Principal Quasi-Submatrices Corresponding to Clusters

Gang Zhang, Zhongjun Ma, Yi Wang and Jianbao Zhang

Abstract and Applied Analysis, 2014, vol. 2014, 1-9

Abstract:

A partial synchronization problem in an oscillator network is considered. The concept on a principal quasi-submatrix corresponding to the topology of a cluster is proposed for the first time to study partial synchronization. It is shown that partial synchronization can be realized under the condition depending on the principal quasi-submatrix, but not distinctly depending on the intercluster couplings. Obviously, the dimension of any principal quasi-submatrix is usually far less than the one of the network topology matrix. Therefore, our criterion provides us a novel index of partial synchronizability, which reduces the network size when the network is composed of a great mount of nodes. Numerical simulations are carried out to confirm the validity of the method.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:584790

DOI: 10.1155/2014/584790

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