JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2017, Vol. 47 ›› Issue (4): 43-49.doi: 10.6040/j.issn.1672-3961.0.2016.122

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Synchronization of time-delayed complex dynamical networks with discontinuous coupling

ZHANG Yuting1,3, LI Wang1,2, WANG Chenguang1, LIU Youquan1, SHI Hongjun1*   

  1. 1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China;
    2. Basic Department, Jiangsu Xuzhou Medical College, Xuzhou 221116, Jiangsu, China;
    3. School of Humanities and Social Science and Law, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China
  • Received:2016-04-13 Online:2017-08-20 Published:2016-04-13

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Abstract: The synchronization problem of complex dynamical networks with time delay and discontinuous coupling was investigated based on Lyapunov stability theory. The sufficient conditions for the networks synchronization was established and the upper bound estimation of the time delay was obtained. The acquired analytical results showed that network with discontinuous coupling could achieve synchronization if time delay met some conditions. The upper bound of the delay for synchronization depended on the coupling strength, the algebraic connectivity of network and on-off rate. The application of numerical simulation results proved that evolution trajectory of network synchronization error and different conditions, in which Ikeda system was used as node dynamics and error function as the network synchronization index. Furthermore, the effect of control parameters on the synchronization speed was analyzed. Numerical examples were provided to verify the effectiveness of the theoretical results.

Key words: discontinuous coupling, synchronization, Lyapunov stability theory, complex networks, time delay

CLC Number: 

  • TP273
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