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具有类万有引力的有界置信观点动力学分析与应用

刘青松 习晓苗 柴利

刘青松, 习晓苗, 柴利. 具有类万有引力的有界置信观点动力学分析与应用. 自动化学报, 2022, 48(x): 1−9 doi: 10.16383/j.aas.c211134
引用本文: 刘青松, 习晓苗, 柴利. 具有类万有引力的有界置信观点动力学分析与应用. 自动化学报, 2022, 48(x): 1−9 doi: 10.16383/j.aas.c211134
Liu Qing-Song, Xi Xiao-Miao, Chai Li. Analysis and application of bounded confidence opinion dynamics with universal gravitation-like. Acta Automatica Sinica, 2022, 48(x): 1−9 doi: 10.16383/j.aas.c211134
Citation: Liu Qing-Song, Xi Xiao-Miao, Chai Li. Analysis and application of bounded confidence opinion dynamics with universal gravitation-like. Acta Automatica Sinica, 2022, 48(x): 1−9 doi: 10.16383/j.aas.c211134

具有类万有引力的有界置信观点动力学分析与应用

doi: 10.16383/j.aas.c211134
基金项目: 国家自然科学基金(61903282, 62173259), 中国博士后科学基金(2020T130488)资助
详细信息
    作者简介:

    刘青松:武汉科技大学信息科学与工程学院副教授. 2019年获哈尔滨工业大学博士学位. 主要研究方向为社会网络, 观点动力学分析, 时滞系统和多智能体系统. E-mail: qingsongliu@wust.edu.cn

    习晓苗:武汉科技大学信息科学与工程学院硕士研究生. 2020年获湖南科技大学学士学位. 主要研究方向为社会网络和观点动力学分析. E-mail: xixiaomiaoivy@163.com

    柴利:武汉科技大学信息科学与工程学院教授. 2002年获香港科技大学博士学位. 主要研究方向为分布式优化, 滤波器组框架, 图信号处理和网络化控制系统. 本文通信作者. E-mail: chaili@wust.edu.cn

Analysis and Application of Bounded Confidence Opinion Dynamics With Universal Gravitation-like

Funds: Supported by National Natural Science Foundation of China (61903282, 62173259), China Postdoctoral Science Foundation (2020T130488)
More Information
    Author Bio:

    LIU Qing-Song Associate professor at the School of Information Science and Engineering, Wuhan University of Science and Technology. He received his Ph.D. degree from Harbin Institute of Technology in 2019. His research interest covers social networks, opinion dynamics analysis, time-delay systems and multiagent systems

    XI Xiao-Miao Master student at the School of Information Science and Engineering, Wuhan University of Science and Technology. She received her bachelor degree from Hunan University of Science and Technology in 2020. Her research interest covers social networks and opinion dynamics analysis

    CHAI Li Professor at the School of Information Science and Engineering, Wuhan University of Science and Technology. He received his Ph.D. degree from Hong Kong University of Science and Technology in 2002. His research interest covers distributed optimization, filter bank frames, graph signal processing and networked control systems. Corresponding author of this paper

  • 摘要: 在社会网络中, Hegselmann-Krause模型描述了置信阈值内不同邻居对个体的观点影响权重都是相同的, 且邻居对个体的吸引力与他们的观点差值成正比, 这是不切实际的. 为了克服经典Hegselmann-Krause模型的不足, 提出了具有类万有引力的有界置信观点动力学模型, 描述个体观点的更新依赖于观点之间的差值和邻居的权威性, 且不同邻居对个体的观点影响权重不同. 根据置信矩阵的性质证明观点的收敛性, 并分析具有衰减置信阈值的观点动力学行为, 给出观点收敛速率的显式解. 最后, 利用本文提出的观点动力学模型研究社会心理学中的“权威效应”和“非零和效应”. 仿真分析表明, 邻居的权威性有利于观点达成一致.
  • 图  1  $d_{ij}(k)$关于$\vert N_j\vert$$x_j(k)-x_i(k)$的函数图

    Fig.  1  The trajectories of $d_{ij}(k)$ with respect to $\vert N_j\vert$ and $x_j(k)-x_i(k)$

    图  2  个体$j$对个体$i$观点的影响

    Fig.  2  The influence of individual $j$ on the opinion of individual $i$

    图  3  网络拓扑结构 (个体4为权威个体)

    Fig.  3  Network structure (individual 4 is the authoritative individual)

    图  4  权威效应 (个体4为权威个体)

    Fig.  4  Authority effect (individual 4 is the authoritative individual)

    图  5  网络拓扑结构 (个体5为权威个体)

    Fig.  5  Network structure (individual 5 is the authoritative individual)

    图  6  权威效应 (个体5为权威个体)

    Fig.  6  Authority effect (individual 5 is the authoritative individual)

    图  7  非零和效应

    Fig.  7  Sum non-zero effect

    图  8  初值为均匀分布时的观点演化

    Fig.  8  Opinion evolution when the initial value is uniformly distributed

    图  9  初值为正态分布时的观点演化

    Fig.  9  Opinion evolution when the initial value is normally distributed

    图  10  模型(10)观点演化

    Fig.  10  Opinion evolution of model (10)

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  • 收稿日期:  2021-11-30
  • 录用日期:  2022-04-28
  • 网络出版日期:  2022-05-30

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