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

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
[1] WATTS D J, STROGATZ S H. Collective dynamics of small-world networks[J]. Nature, 1998, 393(6684):440-442.
[2] BARABÁSIA L, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512.
[3] 郭雷, 许晓鸣. 复杂网络[M]. 上海:上海科技教育出版社, 2006.
[4] 汪小帆, 李翔, 陈关荣. 复杂网络理论及其应用[M]. 北京:清华大学出版社, 2006.
[5] ARENAS A, DÍAZ-GUILERA A, KURTHS J, et al. Synchronization in complex networks[J]. Physics Reports, 2008, 469(3): 93-153.
[6] 何大韧, 刘宗华, 汪秉宏. 复杂系统与复杂网络[M]. 北京: 高等教育出版社, 2009.
[7] 赵永清, 江明辉. 混合变时滞二重边复杂网络自适应同步反馈控制[J]. 山东大学学报(工学版), 2010, 40(3):61-68. ZHAO Yongqing, JIANG Minghui. Adaptive synchronous feedback control of mixed time-varying delayed and double-linked complex networks[J]. Journal of Shangdong University(Engineering Science), 2010, 40(3):61-68.
[8] 李望, 石咏, 马继伟. 复杂动态网络的有限时间外部同步[J]. 山东大学学报(工学版), 2013, 43(2):61-68. LI Wang, SHI Yong, MA Jiwei. Finite-time outer synchronization of complex dynamical networks[J]. Journal of Shangdong University(Engineering Science), 2013, 43(2):61-68.
[9] 孙炜伟, 王玉振. 几类时滞非线性哈密顿系统的稳定性分析[J]. 山东大学学报(理学版), 2007, 42(12):1-9. SUN Weiwei, WANG Yuzhen. Stability analysis for some classes of time-delay nonlinear Hamiltonian systems[J]. Journal of Shangdong University(Natural Science), 2007, 42(12):1-9.
[10] PECORA L M, CARROLL T L. Master stability functions for synchronized coupled systems[J]. Physical Review Letters, 1998, 80(10): 2109-2112.
[11] WANG Xiaofan, CHEN Guanrong. Synchronization in small-world dynamical networks[J]. International Journal of Bifurcation & Chaos, 2002, 12(1):187-192.
[12] WANG Xiaofan, CHEN Guanrong. Synchronization in scale-free dynamical networks: robustness and fragility[J]. IEEE Transactions on Circuits System I, 2002, 49(1):54-62.
[13] LU Jinhu, CHEN Guanrong. A time-varying complex dynamical network model and its controlled synchronization criteria[J]. IEEE Transactions on Automatic Control, 2005, 50(6):841-846.
[14] WU Xiaoqun, ZHENG Weixing, ZHOU Jin. Generalized outer synchronization between complex dynamical networks[J]. Chaos an Interdisciplinary Journal of Nonlinear Science, 2009, 19(1):193-204.
[15] 涂俐兰, 陆君安. 一类时滞动力网络的时滞相关稳定性[J]. 复杂系统与复杂性科学, 2007, 4(2):33-38. TU Lilan, LU Junan. Delay-dependent stability conditrons in general concplex delayed dynamical networks[J]. Complex System and Complexity Science, 2007, 4(2):33-38.
[16] ZHANG Lixian, BOUKAS E K, LAM J. Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities[J]. IEEE Transactions on Automatic Control, 2008, 53(10):2458-2464.
[17] CHIOU J S. Stability analysis for a class of switched large-scale time-delay systems via time-switched method[J]. IEEE Proceedings: Control Theory and Applications, 2006, 153(6):684-688.
[18] CAO Jinde, WANG Zidong, SUN Yonghui. Synchronization in an array of of linearly stochastically coupled networks with time delay[J]. Physica A, 2007, 385(2): 718-728.
[19] YU Wenwu, CAO Jinde. Synchronization control of stochastic delayed neural networks[J]. Physica A, 2007, 373(1):252-260.
[20] HUNT D, KOMISS G, SZYMANSKI B K. Network synchronization in a noisy environment with time delays: fundamental limits and trade-offs[J]. Physical Review Letters, 2010, 105(6):2155-2212.
[21] CHEN Liquan, QIU Chengfeng, HUANG H B. Synchronization with on-off coupling: role of time scales in network dynamics[J]. Physical Review E: Statistical Nonlinear & Soft Matter Physics, 2009, 79(4 Pt 2):045-101.
[22] CHEN Liquan, QIU Chengfeng, HUANG H B. Facilitated synchronization of complex networks through a discontinuous coupling strategy[J]. The European Physical Journal B, 2010, 76(4):625-635.
[23] SUN Yongzheng, WANG Li, ZHAO Donghua. Outer synchronization between two complex dynamical networks with discontinuous coupling[J]. Chaos an Interdisciplinary Journal of Nonlinear Science, 2012, 22(4):517-525.
[24] 张颖, 段广仁. 时滞离散切换系统基于观测器的输出反馈镇定[J]. 山东大学学报(工学版), 2005, 35(3):40-43. ZHANG Ying, DUAN Guangren. Observer-based output feedback stabilization for a class of discrete-time switched systems with time-delay[J]. Journal of Shangdong University(Engineering Science), 2005, 35(3):40-43.
[25] ZHOU Jin, CHEN Tianping. Synchronization in general complex delayed dynamical networks[J]. Circuits & Systems I Regular Papers IEEE Transactions on, 2006, 53(3):733-744.
[26] CHIOU J, WANG C, CHENG Chunming. On delay-dependent stabilization analysis for the switched time-delay systems with the state-driven switching strategy[J]. Journal of the Franklin Institute, 2011, 348(9):2292-2307.
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