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The Optimum Of Synchronizability In Complex Networks

Author

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  • PEI-JIE MA

    (Department of Modern Physics, University of Science and Technology of China, Hefei 230026, P. R. China;
    Complex System Research Center, University of Shanghai for Science and Technology, and Shanghai Academy of System Science, Shanghai 200093, P. R. China)

  • BING-HONG WANG

    (Department of Modern Physics, University of Science and Technology of China, Hefei 230026, P. R. China;
    Complex System Research Center, University of Shanghai for Science and Technology, and Shanghai Academy of System Science, Shanghai 200093, P. R. China)

Abstract

In this brief report, we investigate the synchronizability of the complex network. In order to optimize the synchronizability, we propose a method by introducing a weight matrix, which makes the synchronized states stable for the widest range of the overall coupling strength. We give a proof in mathematics and gain the exact form of the weight matrix, which is equal toLβ. MatrixLis the one that describes the optimal network and matrix β is constructed by the eigenvalues and eigenvectors of the usual Laplacian matrix. This result may provide us insight into the synchronization of complex network more deeply.

Suggested Citation

  • Pei-Jie Ma & Bing-Hong Wang, 2010. "The Optimum Of Synchronizability In Complex Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 21(10), pages 1255-1261.
    • Handle: RePEc:wsi:ijmpcx:v:21:y:2010:i:10:n:s0129183110015816
    DOI: 10.1142/S0129183110015816
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    Cited by:

    1. Zihan Tan, 2016. "On the computational complexity of bridgecard," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 196-217, January.

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