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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (11): 53-60.doi: 10.6040/j.issn.1671-9352.0.2022.322

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基于变量替换控制的分数阶复杂网络拓扑识别

马维元1(),李志明2,代常平1   

  1. 1. 西北民族大学数学与计算机科学学院, 甘肃 兰州 730030
    2. 贵州航天天马机电科技有限公司，贵州 遵义 563000
  • 收稿日期:2022-05-30 出版日期:2023-11-20 发布日期:2023-11-07
  • 作者简介:马维元(1980—)，男，副教授，博士，硕士生导师，研究方向为分数阶复杂网络及同步. E-mail: mwy2004@126.com
  • 基金资助:
    国家自然科学基金资助项目(61966032);甘肃省自然科学基金资助项目(22JR5RA184);中央高校基本科研业务费项目(31920220041)

Topology identification of fractional complex networks based on variable substitution control method

Weiyuan MA1(),Zhiming LI2,Changping DAI1   

  1. 1. School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
    2. Guizhou Aerospace Tianma Electromechanical Technology Co., Ltd., Zunyi 563000, Guizhou, China
  • Received:2022-05-30 Online:2023-11-20 Published:2023-11-07

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摘要：

研究了基于可变替换控制法的分数阶复杂动力学网络的同步及拓扑辨识问题，构造了具有可变替换控制的响应网络和参数更新律，利用分数阶微分系统稳定性理论，推导了实现拓扑识别和同步的准则。最后通过数值仿真验证了所提方法的有效性和可行性。

关键词: 变量替换控制, 拓扑识别, 同步, 复杂网络

Abstract:

In this paper, synchronization and topology identification of fractional-order complex dynamical networks based on the variable substitution control method are studied. The considered network constructs a response network and parameter update law with variable substitution control. Based on the stability theory of fractional differential systems, the criteria for realizing topology identification and synchronization are deduced. Finally, the effectiveness and feasibility of the proposed method are verified by numerical simulation.

Key words: variable substitution control, topology identification, synchronization, complex network

中图分类号: 

  • N941.4

图1

例1中未知拓扑结构随时间的演化效果"

图2

例1中的同步误差"

图3

例1中的不同分数阶阶数下的总体平均误差"

图4

例2中未知拓扑结构的识别效果"

图5

例2中的同步误差"

图6

例2中的不同分数阶阶数下的总体平均误差"

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