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忆阻突触耦合Hopfield神经网络的初值敏感动力学

陈墨 陈成杰 包伯成 徐权

引用本文: 陈墨, 陈成杰, 包伯成, 徐权. 忆阻突触耦合Hopfield神经网络的初值敏感动力学[J]. 电子与信息学报, doi: 10.11999/JEIT190858 shu
Citation:  Mo CHEN, Chengjie CHEN, Bocheng BAO, Quan XU. Initial Sensitive Dynamics in Memristor Synapse-coupled Hopfield Neural Network[J]. Journal of Electronics and Information Technology, doi: 10.11999/JEIT190858 shu

忆阻突触耦合Hopfield神经网络的初值敏感动力学

    作者简介: 陈墨: 女,1982年生,副教授,研究方向为忆阻电路与系统、类脑计算与神经网络;
    陈成杰: 男,1996年生,硕士生,研究方向为类脑计算与神经网络、神经混沌动力学;
    包伯成: 男,1965年生,教授,研究方向为忆阻电路与系统、混沌信息动力学和类脑计算与神经网络;
    徐权: 男,1983年生,副教授,研究方向为非自治混沌电路与系统、类脑计算与神经网络
    通讯作者: 陈墨,mchen@cczu.edu.cn
  • 基金项目: 国家自然科学基金(51777016, 61801054, 61601062),江苏省研究生科研与实践创新计划项目(KYCX19_1767)

摘要: 该文报道了3神经元Hopfield神经网络(HNN)在电磁感应电流作用下的初值敏感动力学。利用非理想忆阻突触,模拟由两个相邻神经元膜电位之差引起的电磁感应电流,构建了一种简单的4维忆阻Hopfield神经网络模型。借助理论分析和数值仿真,分析了不同忆阻突触耦合强度下的复杂动力学行为,揭示了与状态初值密切相关的特殊动力学行为。最后,设计了该忆阻HNN的模拟等效实现电路,并由PSIM电路仿真验证了MATLAB数值仿真的正确性。

English

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  • 图 1  基于非理想忆阻突触的HNN的连接拓扑

    图 2  不同忆阻耦合强度时H1(y, z)和H2(y, z)函数曲线及交点平衡点

    图 3  不同初值下随参数k变化的共存分岔行为

    图 4  不同忆阻耦合强度下x1x3平面上的相轨图

    图 5  状态变量x1随状态初值变化的分岔图

    图 6  不同忆阻耦合强度下x1(0)–x2(0)平面的吸引盆

    图 7  不同忆阻耦合强度下共存吸引子在x1x3平面的相轨图

    图 8  忆阻HNN模型(2)的等效实现电路

    图 9  PSIM电路仿真得到的共存吸引子在v1x3平面上的相轨图

    表 1  k=–1, 0和1时的平衡点及其特征值和稳定性

    k平衡点特征值稳定性
    –1P0: (0, 0, 0, 0)1.6062, –0.9531±j2.3986, –1不稳定指数1鞍焦
    P1: (–0.0019, –0.1689, 3.3462, 0.1670)0.0981±j2.0026, –0.8763, –0.9875不稳定指数2鞍焦
    P2: (0.0369, 0.1814, –3.5887, –0.1445)0.5146±j2.0051, –0.9923, –1.0882不稳定指数2鞍焦
    P3: (0.9448, 2.5018, –19.7332, –1.5570)3.4659, –0.9464, –1, –1.6894不稳定鞍点
    0P0: (0, 0, 0, 0)1.6062, –0.9531±j2.3986, –1不稳定指数1鞍焦
    P1: (0.0220, 0.1761, –3.4860, –0.1541)0.3267±j2.0074, –0.9906, –1不稳定指数2鞍焦
    P2: (–0.0220, –0.1761, 3.4860, 0.1541)0.3267±j2.0074, –0.9906, –1不稳定指数2鞍焦
    1P0: (0, 0, 0, 0)1.6062, –0.9531±j2.3986, –1不稳定指数1鞍焦
    P1: (–0.9448, –2.5018, 19.7332, 1.5570)3.4659, –0.9464, –1, –1.6894不稳定鞍点
    P2: (–0.0369, –0.1814, 3.5887, 0.1445)0.5146±j2.0051, –0.9923, –1.0882不稳定指数2鞍焦
    P3: (0.0019, 0.1689, –3.3462, –0.1670)0.0981±j2.0026, –0.8763, –0.9875不稳定指数2鞍焦
    下载: 导出CSV

    表 2  图7中不同颜色吸引子对应的初值及吸引子类型

    颜色k=0.6k=–0.5吸引子类型
    (–10–6, 0, 0, 0)(0, –10–9, 0, 0)周期吸引子
    (10–6, 0, 0, 0)(0, 10–9, 0, 0)多周期吸引子
    (10–5, 0, 0, 0)(0, 10–7, 0, 0)混沌吸引子
    (1, 0, 0, 0)(0, –2, 0, 0)发散
    (0, 5, 0, 0)发散
    下载: 导出CSV
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文章相关
  • 通讯作者:  陈墨, mchen@cczu.edu.cn
  • 收稿日期:  2019-11-01
  • 录用日期:  2020-01-20
  • 网络出版日期:  2020-03-13
通讯作者: 陈斌, bchen63@163.com
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