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Synchronization of complex dynamical networks with time delays

Author

Listed:
  • Li, C.P.
  • Sun, W.G.
  • Kurths, J.

Abstract

In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems.

Suggested Citation

  • Li, C.P. & Sun, W.G. & Kurths, J., 2006. "Synchronization of complex dynamical networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 24-34.
  • Handle: RePEc:eee:phsmap:v:361:y:2006:i:1:p:24-34
    DOI: 10.1016/j.physa.2005.07.007
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    References listed on IDEAS

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    1. Martı́, Arturo C. & Masoller, C., 2004. "Synchronization of globally coupled non-identical maps with inhomogeneous delayed interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 344-350.
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    Citations

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    Cited by:

    1. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
    2. 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.
    3. Wu, Zhaoyan, 2015. "Synchronization of discrete dynamical networks with non-delayed and delayed coupling," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 57-62.
    4. Feng, Jianwen & Yang, Pan & Zhao, Yi, 2016. "Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 52-68.
    5. Rakkiyappan, R. & Velmurugan, G. & Nicholas George, J. & Selvamani, R., 2017. "Exponential synchronization of Lur’e complex dynamical networks with uncertain inner coupling and pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 217-231.
    6. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.
    7. Wu, Hao & Jiang, Huijun & Hou, Zhonghuai, 2011. "Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 836-844.
    8. Dai, Yang & Cai, Yunze & Xu, Xiaoming, 2008. "Synchronization criteria for complex dynamical networks with neutral-type coupling delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4673-4682.
    9. Hongjie Li & W. K. Wong & Yang Tang, 2012. "Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 496-516, February.
    10. 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.
    11. Liu, Z.X. & Chen, Z.Q. & Yuan, Z.Z., 2007. "Pinning control of weighted general complex dynamical networks with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 345-354.
    12. Liang, Song & Wu, Ranchao & Chen, Liping, 2016. "Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 49-62.
    13. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.

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