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山东大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (3): 1-8.doi: 10.6040/j.issn.1672-3961.0.2016.320

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时滞复杂动态网络的有限时间随机广义外部同步

李望1,2,马志才2,侍红军2   

  1. 1. 江苏徐州医药高等职业学校基础部, 江苏 徐州 221116;2. 中国矿业大学数学学院, 江苏 徐州 221116
  • 收稿日期:2016-08-04 出版日期:2017-06-20 发布日期:2016-08-04
  • 作者简介:李望(1979— ),女,江苏徐州人,讲师,工学硕士,主要研究方向为复杂系统仿真.E-mail:liwang718@126.com
  • 基金资助:
    国家自然科学基金资助项目(61403393);中央高校基本科研业务费资助项目(2015XKMS076)

Finite-time stochastic generalized outer synchronization of time-delayed complex dynamical networks

LI Wang1,2, MA Zhicai2, SHI Hongjun2   

  1. 1. Basic Department, Jiangsu Xuzhou Medical College, Xuzhou 221008, Jiangsu, China;
    2. School of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China
  • Received:2016-08-04 Online:2017-06-20 Published:2016-08-04

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摘要： 基于有限时间控制技术以及开环控制技术,研究具有噪声干扰的时滞复杂动态网络的有限时间广义外部同步问题。设计新的有限时间控制器,利用随机微分方程的稳定性理论得到网络实现有限时间随机广义外部同步的充分条件。研究表明:设计的控制器对于噪声干扰具有较强的鲁棒性,且网络同步时间与控制强度密切相关。在其他条件不变的情况下,网络同步时间随着控制强度的增大而减小。数值模拟中分别选择R(¨overo)ssler-like系统和Hindmarsh-Rose系统作为驱动网络与响应网络的节点动力学,给出了网络同步误差和总同步误差的演化轨迹。数值模拟结果验证了理论结果的有效性与可行性。

关键词: 噪声, 同步, 复杂网络, 时滞

Abstract: Based on the finite-time control technology and the open-loop control method, the generalized outer synchronization between two complex dynamical networks with time delay and noise perturbation was investigated. A new finite-time controller was designed and the sufficient condition for the finite-time stochastic generalized outer synchronization was obtained based on the finite-time stability theory of stochastic differential equations. The results showed that the synchronization scheme was robust to the noise perturbation. The theoretical results showed that the synchronization time depended on the control strength. Under the same conditions, the synchronization time decreased with the increasing of the control strength. In the numerical examples, the R(¨overo)ssler-like system and Hindmarsh-Rose system were chosen as the node dynamics of the drive and response networks, respectively. The time evolution trajectories of synchronization error and total synchronization error were given. The effectiveness and feasibility of the theoretical result was confirmed by the numerical results.

Key words: complex networks, noise, synchronization, time delay

中图分类号: 

  • TP13
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