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大规模超环神经网络分岔动力学

张跃中 肖敏 王璐 徐丰羽

张跃中, 肖敏, 王璐, 徐丰羽. 大规模超环神经网络分岔动力学. 自动化学报, 2020, 46(x): 1−8 doi: 10.16383/j.aas.c200130
引用本文: 张跃中, 肖敏, 王璐, 徐丰羽. 大规模超环神经网络分岔动力学. 自动化学报, 2020, 46(x): 1−8 doi: 10.16383/j.aas.c200130
Zhang Yue-Zhong, Xiao Min, Wang Lu, Xu Feng-Yu. Bifurcation dynamics of large-scale neural networks composed of super multi ring networks. Acta Automatica Sinica, 2020, 46(x): 1−8 doi: 10.16383/j.aas.c200130
Citation: Zhang Yue-Zhong, Xiao Min, Wang Lu, Xu Feng-Yu. Bifurcation dynamics of large-scale neural networks composed of super multi ring networks. Acta Automatica Sinica, 2020, 46(x): 1−8 doi: 10.16383/j.aas.c200130

大规模超环神经网络分岔动力学

doi: 10.16383/j.aas.c200130
基金项目: 国家自然科学基金(62073172, 61573194, 51775284), 江苏省自然科学基金(BK20181389)资助
详细信息
    作者简介:

    张跃中:南京邮电大学自动化学院、人工智能学院硕士研究生. 主要研究方向为神经网络动力学. E-mail: m13255191236@163.com

    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

    王璐:南京邮电大学自动化学院、人工智能学院硕士研究生. 主要研究方向为信息物理融合系统. E-mail: wangdadeer@aliyun.com

    徐丰羽:南京邮电大学自动化学院、人工智能学院教授. 主要研究方向为机器人及其自动化. E-mail: xufengyu598@163.com

Bifurcation Dynamics of Large-scale Neural Networks Composed of Super Multi Ring Networks

Funds: Supported by National Natural Science Foundation of China (62073172, 61573194, 51775284) and Natural Science Foundation of Jiangsu Province (BK20181389)
  • 摘要: 目前绝大多数神经网络分岔动力学局限于结构简单、低维少节点模型, 这与真实的大规模神经网络系统相去甚远. 因此, 研究大量神经元耦合的高维神经网络模型更具实际应用价值. 环状及辐射状结构在神经网络中普遍存在, 本文提出了一类大规模超环时滞神经网络模型, 其结构包含一个大环和任意多个小环, 并且每个环上拥有任意多个神经元. 运用特征值法和分岔理论, 选取时滞为分岔参数, 给出了该超环神经网络模型的稳定性条件和Hopf分岔判据. 数值仿真验证我们理论结果的正确性.
  • 图  1  一类融合多种结构的超环神经网络模型图

    Fig.  1  Model diagram of a class of super multi ring neural network fused with multiple structures

    图  2  $\tau = 3.15 < {\tau _0}$ 时, 网络(15)渐近稳定.

    Fig.  2  When $\tau = 3.15 < {\tau _0}$ , network (15) is asymptotically stable.

    图  3  $\tau = 3.3 > {\tau _0}$ 时, 网络(15)失稳.

    Fig.  3  Network (15) is unstable when $\tau = 3.3 > {\tau _0}$ .

    表  1  网络(15)的初始参数设定表

    Table  1  Initial parameter setting table for network (15)

    参数 $\rho $ $v_j^{(k)},\forall j,k = \overline {1,3} $
    初始值 0.75 -0.6
    下载: 导出CSV

    表  2  结构变化影响分岔点位置情况表

    Table  2  Table of the influence of structural change on the location of bifurcation points

    环的个数 结构简图 神经元个数 分岔点
    3 6 16.2
    4 9 3.22
    5 12 2.08
    下载: 导出CSV
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  • 收稿日期:  2020-03-17
  • 录用日期:  2020-09-07

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