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, issue 1

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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https://doi.org/10.1155/2014/584790

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:584790

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