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Pinning synchronization of delayed complex dynamical networks with nonlinear coupling

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  • Cheng, Ranran
  • Peng, Mingshu
  • Yu, Weibin

Abstract

In this paper, we find that complex networks with the Watts–Strogatz or scale-free BA random topological architecture can be synchronized more easily by pin-controlling fewer nodes than regular systems. Theoretical analysis is included by means of Lyapunov functions and linear matrix inequalities (LMI) to make all nodes reach complete synchronization. Numerical examples are also provided to illustrate the importance of our theoretical analysis, which implies that there exists a gap between the theoretical prediction and numerical results about the minimum number of pinning controlled nodes.

Suggested Citation

  • Cheng, Ranran & Peng, Mingshu & Yu, Weibin, 2014. "Pinning synchronization of delayed complex dynamical networks with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 426-431.
    • Handle: RePEc:eee:phsmap:v:413:y:2014:i:c:p:426-431
    DOI: 10.1016/j.physa.2014.06.034
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    References listed on IDEAS

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    1. Xiang, L.Y. & Liu, Z.X. & Chen, Z.Q. & Chen, F. & Yuan, Z.Z., 2007. "Pinning control of complex dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 298-306.
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    5. 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.
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    Cited by:

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    2. Wang, Jian-an & Ma, Xiaohui & Wen, Xinyu & Sun, Qianlai, 2016. "Pinning lag synchronization of drive–response complex networks via intermittent control with two different switched periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 278-287.
    3. Cheng, Ranran & Peng, Mingshu & Zuo, Jun, 2016. "Pinning synchronization of discrete dynamical networks with delay coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 444-453.
    4. Zhang, Chuan & Wang, Xingyuan & Luo, Chao & Li, Junqiu & Wang, Chunpeng, 2018. "Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 251-264.
    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. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    7. Wenhua Xia & Yiping Luo & Bifeng Zhou & Guanghui Liu, 2017. "Exponential Synchronization of a Class of -Coupled Complex Partial Differential Systems with Time-Varying Delay," Complexity, Hindawi, vol. 2017, pages 1-9, October.
    8. Yi-Ping Luo & Li Shu & Bi-Feng Zhou, 2017. "Global Exponential Synchronization of Nonlinearly Coupled Complex Dynamical Networks with Time-Varying Coupling Delays," Complexity, Hindawi, vol. 2017, pages 1-10, August.

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