Partial Synchronizability Characterized by Principal Quasi-Submatrices Corresponding to Clusters. (16th July 2014)

• Record Type: Journal Article
• Authors: Zhang, Gang; Ma, Zhongjun; Wang, Yi; Zhang, Jianbao
• Other Names: Hu Jun Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-07-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/584790
• Languages: English
• ISSNs: 1085-3375

Abstract

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.