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Synchronization in complex clustered networks

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Abstract

Synchronization in complex networks has been an active area of research in recent years. While much effort has been devoted to networks with the small-world and scale-free topology, structurally they are often assumed to have a single, densely connected component. Recently it has also become apparent that many networks in social, biological, and technological systems are clustered, as characterized by a number (or a hierarchy) of sparsely linked clusters, each with dense and complex internal connections. Synchronization is fundamental to the dynamics and functions of complex clustered networks, but this problem has just begun to be addressed. This paper reviews some progress in this direction by focusing on the interplay between the clustered topology and network synchronizability. In particular, there are two parameters characterizing a clustered network: the intra-cluster and the inter-cluster link density. Our goal is to clarify the roles of these parameters in shaping network synchronizability. By using theoretical analysis and direct numerical simulations of oscillator networks, it is demonstrated that clustered networks with random inter-cluster links are more synchronizable, and synchronization can be optimized when inter-cluster and intra-cluster links match. The latter result has one counterintuitive implication: more links, if placed improperly, can actually lead to destruction of synchronization, even though such links tend to decrease the average network distance. It is hoped that this review will help attract attention to the fundamental problem of clustered structures/synchronization in network science.

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Authors and Affiliations

  1. Department of Electrical Engineering, Arizona State University, Tempe, Arizona, 85287, USA

    Huang Liang, Lai Ying-Cheng & Kwangho Park

  2. Department of Physics and Astronomy, Arizona State University, Tempe, Arizona, 85287, USA

    Lai Ying-Cheng

  3. Temasek Laboratories, National University of Singapore, Singapore, 117508, Singapore

    Wang Xingang

  4. Beijing-Hong Kong-Singapore Joint Centre for Nonlinear & Complex Systems (Singapore), National University of Singapore, Kent Ridge Singapore, 119260, Singapore

    Wang Xingang & Lai Choy Heng

  5. Department of Physics, National University of Singapore, Singapore, 117542, Singapore

    Lai Choy Heng

  6. Department of Radiology and Applied Mathematics, University of Arizona, Tucson, Arizona, 85721, USA

    Robert A. Gatenby

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  1. Huang Liang
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  2. Lai Ying-Cheng
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  3. Kwangho Park
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  4. Wang Xingang
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Correspondence to Lai Ying-Cheng.

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Huang, L., Lai, YC., Park, K. et al. Synchronization in complex clustered networks. Front. Phys. China 2, 446–459 (2007). https://doi.org/10.1007/s11467-007-0056-x

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  • DOI: https://doi.org/10.1007/s11467-007-0056-x

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