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Synchronization in a class of weighted complex networks with coupling delays

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  • Wang, Qingyun
  • Duan, Zhisheng
  • Chen, Guanrong
  • Feng, Zhaosheng

Abstract

It is commonly accepted that realistic networks can display not only a complex topological structure, but also a heterogeneous distribution of connection weights. In addition, time delay is inevitable because the information spreading through a complex network is characterized by the finite speeds of signal transmission over a distance. Weighted complex networks with coupling delays have been gaining increasing attention in various fields of science and engineering. Some of the topics of most concern in the field of weighted complex networks are finding how the synchronizability depends on various parameters of the network including the coupling strength, weight distribution and delay. On the basis of the theory of asymptotic stability of linear time-delay systems with complex coefficients, the synchronization stability of weighted complex dynamical networks with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of the synchronization state. Finally, an example is given as an illustration testing the theoretical results.

Suggested Citation

  • Wang, Qingyun & Duan, Zhisheng & Chen, Guanrong & Feng, Zhaosheng, 2008. "Synchronization in a class of weighted complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5616-5622.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:22:p:5616-5622
    DOI: 10.1016/j.physa.2008.05.056
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    References listed on IDEAS

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    2. Yun Wang, Qing & Rong Chen, Guan & Shao Lu, Qi & Hao, Fei, 2007. "Novel criteria of synchronization stability in complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 527-536.
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    Cited by:

    1. Zhang, Lili & Wang, Yinhe & Huang, Yuanyuan & Chen, Xuesong, 2015. "Delay-dependent synchronization for non-diffusively coupled time-varying complex dynamical networks," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 510-522.
    2. Su, Lei & Shen, Hao, 2015. "Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 931-942.
    3. M. Saburov & K. Saburov, 2016. "Reaching a consensus: a discrete nonlinear time-varying case," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2449-2457, July.
    4. Zhang, Yan-Jie & Liu, Song & Yang, Ran & Tan, Ying-Ying & Li, Xiaoyan, 2019. "Global synchronization of fractional coupled networks with discrete and distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 830-837.
    5. Tseng, Jui-Pin, 2016. "A novel approach to synchronization of nonlinearly coupled network systems with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 266-280.
    6. Wu, Fuqiang & Kang, Ting & Shao, Yan & Wang, Qingyun, 2023. "Stability of Hopfield neural network with resistive and magnetic coupling," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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