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Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method

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  • Fei Wang
  • Zhaowen Zheng
  • Yongqing Yang

Abstract

This paper investigates the synchronization of general complex dynamical networks (CDNs) with both internal delay and transmission delay. Event-triggered mechanism is applied for the feedback controllers, in which the triggered function is formed as a nonincreasing function. Both continuous feedback and sampled-data feedback methods are studied. According to Lyapunov stability theorem and generalized Halanay’s inequality, quasi-synchronization criteria are derived at first. The synchronization error is bounded with some parameters of the triggered function. Then, the completed synchronization can be guaranteed as a special case. Finally, coupled neural networks as numerical simulation examples are given to verify the theoretical results.

Suggested Citation

  • Fei Wang & Zhaowen Zheng & Yongqing Yang, 2019. "Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method," Complexity, Hindawi, vol. 2019, pages 1-17, December.
    • Handle: RePEc:hin:complx:7348572
    DOI: 10.1155/2019/7348572
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    References listed on IDEAS

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    1. 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.
    2. Zhou, Jiamu & Dong, Hailing & Feng, Jianwen, 2017. "Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 617-629.
    3. Bin Yang & Xin Wang & Yongju Zhang & Yuhua Xu & Wuneng Zhou, 2019. "Finite-Time Synchronization and Synchronization Dynamics Analysis for Two Classes of Markovian Switching Multiweighted Complex Networks from Synchronization Control Rule Viewpoint," Complexity, Hindawi, vol. 2019, pages 1-17, March.
    4. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    5. Bin Yang & Xin Wang & Jian-an Fang & Yuhua Xu, 2019. "The Impact of Coupling Function on Finite-Time Synchronization Dynamics of Multi-Weighted Complex Networks with Switching Topology," Complexity, Hindawi, vol. 2019, pages 1-15, March.
    6. Zeng, Deqiang & Zhang, Ruimei & Liu, Yajuan & Zhong, Shouming, 2017. "Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 34-46.
    7. Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2004. "Chaos synchronization of general complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 281-302.
    8. Wang, Fei & Yang, Yongqing, 2018. "Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 1-14.
    9. Shiyong Zhu & Jungang Lou & Yang Liu & Yuanyuan Li & Zhen Wang, 2018. "Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks," Complexity, Hindawi, vol. 2018, pages 1-7, September.
    10. Zeng, Deqiang & Zhang, Ruimei & Liu, Xinzhi & Zhong, Shouming & Shi, Kaibo, 2018. "Pinning stochastic sampled-data control for exponential synchronization of directed complex dynamical networks with sampled-data communications," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 102-118.
    11. Weiwei Zhang & Jinde Cao & Dingyuan Chen & Ahmed Alsaedi, 2019. "Out Lag Synchronization of Fractional Order Delayed Complex Networks with Coupling Delay via Pinning Control," Complexity, Hindawi, vol. 2019, pages 1-7, August.
    12. Li, Qiaoping & Liu, Sanyang & Chen, Yonggang, 2018. "Combination event-triggered adaptive networked synchronization communication for nonlinear uncertain fractional-order chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 521-535.
    13. 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.
    14. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    15. Fei Wang & Yongqing Yang, 2017. "Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 571-577, February.
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