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神经网络分岔动力学综述

肖敏 陆云翔 虞文武 郑卫新

肖敏, 陆云翔, 虞文武, 郑卫新. 神经网络分岔动力学综述. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230789
引用本文: 肖敏, 陆云翔, 虞文武, 郑卫新. 神经网络分岔动力学综述. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230789
Xiao Min, Lu Yun-Xiang, Yu Wen-Wu, Zheng Wei-Xin. Overview of bifurcation dynamics in neural networks. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230789
Citation: Xiao Min, Lu Yun-Xiang, Yu Wen-Wu, Zheng Wei-Xin. Overview of bifurcation dynamics in neural networks. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c230789

神经网络分岔动力学综述

doi: 10.16383/j.aas.c230789
基金项目: 国家自然科学基金 (62073172, 62233004, 62073076), 江苏省自然科学基金 (BK20221329), 江苏省应用数学科学研究中心 (BK20233002), 江苏省研究生科研与实践创新计划 (KYCX23_1060)资助
详细信息
    作者简介:

    肖敏:南京邮电大学自动化学院、人工智能学院教授. 主要研究方向为非线性控制理论, 复杂网络, 神经网络, 信息网络融合系统, 反常扩散系统. 本文通信作者. E-mail: candymanxm2003@aliyun.com

    陆云翔:南京邮电大学自动化学院、人工智能学院博士研究生. 主要研究方向为神经网络动力学, 非线性控制理论, 反应扩散系统. E-mail: miraclemanlyx@163.com

    虞文武:东南大学数学学院教授. 2010年获得香港城市大学电子工程系博士学位. 主要研究方向为复杂网络系统协同分析, 控制与优化. E-mail: wwyu@seu.edu.cn

    郑卫新:澳大利亚西悉尼大学杰出教授, IEEE Fellow. 主要研究方向为系统辨识, 网络化控制, 多智能体系统, 神经网络, 信号处理. E-mail: w.zheng@westernsydney.edu.au

Overview of Bifurcation Dynamics in Neural Networks

Funds: Supported by National Natural Science Foundation of China (62073172, 62233004, 62073076), Natural Science Foundation of Jiangsu Province of China (BK20221329), Jiangsu Provincial Scientific Research Center of Applied Mathematics (BK20233002), and Practice Innovation Program of Jiangsu Province (KYCX23_1060)
More Information
    Author Bio:

    XIAO Min Professor at the College of Automation & College of Artificial intelligence, Nanjing University of Posts and Telecommunications. His research interest covers nonlinear control theory, complex networks, neural networks, cyber-physical systems, and anomalous diffusion systems. Corresponding author of this paper

    LU Yun-Xiang Ph.D. Candidate at the College of Automation & College of Artificial intelligence, Nanjing University of Posts and Telecommunications. His research interest covers neural networks dynamics, nonlinear control theory, and reaction-diffusion systems

    YU Wen-Wu Professor at the School of Mathematics, Southeast University. He received his Ph.D. degree from the Department of Electrical Engineering, City University of Hong Kong in 2010. His research interest covers collaborative analysis, control and optimization of complex networked systems

    ZHENG Wei-Xin Distinguished Professor at Western Sydney University, Australia. IEEE Fellow. His research interest covers system identification, networked control systems, multi-agent systems, neural networks, and signal processing

  • 摘要: 自1982年著名的Hopfield神经网络问世以来, 神经网络的分岔动力学受到了学术界的广泛关注. 本文回顾了四类经典神经网络的数学模型和它们在各个领域的应用. 接着, 综述了近三十年来关于整数阶神经网络、分数阶神经网络、超数域神经网络以及反应扩散神经网络分岔动力学的相关研究成果. 分析了诸多组合因素, 包括节点规模、耦合情形、拓扑结构、系统阶次、复值、四元数、八元数、扩散、时滞、随机性、脉冲、忆阻、激活函数等对神经网络分岔动力学的影响, 并展示了神经网络在多个领域的广泛应用. 最后, 在人工智能、大数据、深度学习等新技术的冲击下, 对神经网络分岔动力学所面临的挑战以及未来的研究方向进行了总结和展望.
  • 图  1  Hopfield神经网络电路图

    Fig.  1  Circuit of Hopfied neural network

    图  2  细胞神经网络中单个细胞电路图

    Fig.  2  Circuit of a single cell in cellular neural network

    图  3  双向联想记忆神经网络拓扑图

    Fig.  3  Topology of bidirectional associative memory neural network

    图  4  高维耦合下环型拓扑神经网络的发展历程

    Fig.  4  Development of ring topology neural networks under high-dimensional coupling

    图  5  高维耦合下混合型拓扑神经网络的发展历程

    Fig.  5  Development of hybrid topology neural networks under high-dimensional coupling

    表  1  神经网络模型分类

    Table  1  Classification for neural network models

    神经网络类型 代表性文献 应用领域 特点
    IONNs 少节点全连接 [20, 3435] 嵌入式系统
    实时系统
    边缘计算
    低功耗设备
    结构简单, 计算速度较快
    适用于低功耗、资源受限的实时系统
    灵活性不足、精度不高、适用范围受限
    少节点非全连接 [41, 45]
    多节点Ring [7071, 77]
    多节点Star [26, 7879]
    多节点Hybrid [8283]
    FONNs 少节点耦合 [9899, 101] 信号处理
    动态系统建模
    时间序列预测
    具有记忆和遗传特性、适用于非平稳信号处理
    适用于建模复杂的非线性系统和时间序列数据
    计算复杂度较高、训练过程比较困难
    高维耦合 [75, 81, 104]
    SDNNs CVNNs [108, 122, 124] 信号处理
    通信系统
    量子计算
    能够更好地处理复数数据、提高数据表示能力
    训练复杂度较高、需要特殊的数学处理技巧
    QVNNs [125, 127]
    OVNNs [134135]
    RDNNs 少节点耦合 [150, 156157] 模式生成
    自组织系统模拟
    能够模拟物理世界中各类反应扩散过程
    计算复杂度较高、训练过程困难
    高维耦合 [158159, 160]
    下载: 导出CSV
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