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山东大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (4): 43-49.doi: 10.6040/j.issn.1672-3961.0.2016.122

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不连续耦合的时滞复杂动态网络的同步

张玉婷1,3,李望1,2,王晨光1,刘友权1,侍红军1*   

  1. 1. 中国矿业大学数学学院, 江苏 徐州 221116;2. 江苏徐州医药高等学校基础部, 江苏 徐州 221116;3. 哈尔滨工业大学人文社科与法学学院, 黑龙江 哈尔滨 150001
  • 收稿日期:2016-04-13 出版日期:2017-08-20 发布日期:2016-04-13
  • 通讯作者: 侍红军(1979— ),男,江苏淮安人,讲师,博士研究生,主要研究方向为复杂网络同步与控制,图论染色.E-mail:hjshi79@gmail.com E-mail:zhangyutingzjl@163.com
  • 作者简介:张玉婷(1995— ),女,山东邹城人,硕士研究生,主要研究方向为复杂网络同步. E-mail:zhangyutingzjl@163.com
  • 基金资助:
    中央高校基本科研业务费资助项目(2015xkms076);国家级大学生创新创业训练计划资助项目(201710290089)

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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摘要： 基于李雅普诺夫稳定性理论,对不连续耦合的时滞复杂动态网络进行分析,得到网络同步的充分条件,并且给出网络实现同步时滞的上界估计。研究表明:即使网络之间的耦合是不连续的,只要时滞满足一定条件,网络也可以实现同步,且网络容许的时滞上界与耦合强度、网络代数连通性以及耦合的开关率相关。数值模拟中利用Ikeda系统作为节点动力学,采用误差函数作为网络同步性指标,给出网络同步误差演化轨迹和各状态的演化轨迹,并进一步分析控制参数对同步速度的影响,模拟结果验证了理论结果的正确性。

关键词: 同步, 李雅普诺夫稳定性, 复杂网络, 时滞, 不连续耦合

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

中图分类号: 

  • TP273
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