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憶阻突觸耦合Hopfield神經(jīng)網(wǎng)絡(luò)的初值敏感動(dòng)力學(xué)

陳墨,  陳成杰,  包伯成,  徐權(quán)

陳墨, 陳成杰, 包伯成, 徐權(quán). 憶阻突觸耦合Hopfield神經(jīng)網(wǎng)絡(luò)的初值敏感動(dòng)力學(xué)[J]. 電子與信息學(xué)報(bào), 2020, 42(4): 870-877. doi: 10.11999/JEIT190858
引用本文: 陳墨, 陳成杰, 包伯成, 徐權(quán). 憶阻突觸耦合Hopfield神經(jīng)網(wǎng)絡(luò)的初值敏感動(dòng)力學(xué)[J]. 電子與信息學(xué)報(bào), 2020, 42(4): 870-877. doi: 10.11999/JEIT190858
Mo CHEN, Chengjie CHEN, Bocheng BAO, Quan XU. Initial Sensitive Dynamics in Memristor Synapse-coupled Hopfield Neural Network[J]. Journal of Electronics & Information Technology, 2020, 42(4): 870-877. doi: 10.11999/JEIT190858
Citation: Mo CHEN, Chengjie CHEN, Bocheng BAO, Quan XU. Initial Sensitive Dynamics in Memristor Synapse-coupled Hopfield Neural Network[J]. Journal of Electronics & Information Technology, 2020, 42(4): 870-877. doi: 10.11999/JEIT190858

憶阻突觸耦合Hopfield神經(jīng)網(wǎng)絡(luò)的初值敏感動(dòng)力學(xué)

doi: 10.11999/JEIT190858

  • 常州大學(xué)信息科學(xué)與工程學(xué)院 常州 213164

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(51777016, 61801054, 61601062)，江蘇省研究生科研與實(shí)踐創(chuàng)新計(jì)劃項(xiàng)目(KYCX19_1767)
詳細(xì)信息
    作者簡(jiǎn)介:

    陳墨：女，1982年生，副教授，研究方向?yàn)閼涀桦娐放c系統(tǒng)、類腦計(jì)算與神經(jīng)網(wǎng)絡(luò)

    陳成杰：男，1996年生，碩士生，研究方向?yàn)轭惸X計(jì)算與神經(jīng)網(wǎng)絡(luò)、神經(jīng)混沌動(dòng)力學(xué)

    包伯成：男，1965年生，教授，研究方向?yàn)閼涀桦娐放c系統(tǒng)、混沌信息動(dòng)力學(xué)和類腦計(jì)算與神經(jīng)網(wǎng)絡(luò)

    徐權(quán)：男，1983年生，副教授，研究方向?yàn)榉亲灾位煦珉娐放c系統(tǒng)、類腦計(jì)算與神經(jīng)網(wǎng)絡(luò)

    通訊作者:

    陳墨　mchen@cczu.edu.cn

  • 中圖分類號(hào): TN601; TN711.4

Initial Sensitive Dynamics in Memristor Synapse-coupled Hopfield Neural Network

  • School of Information Science and Engineering, Changzhou University, Changzhou 213164, China

Funds: The National Natural Science Foundation of China (51777016, 61801054, 61601062), The Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (KYCX19_1767)
  • 摘要: 該文報(bào)道了3神經(jīng)元Hopfield神經(jīng)網(wǎng)絡(luò)(HNN)在電磁感應(yīng)電流作用下的初值敏感動(dòng)力學(xué)。利用非理想憶阻突觸，模擬由兩個(gè)相鄰神經(jīng)元膜電位之差引起的電磁感應(yīng)電流，構(gòu)建了一種簡(jiǎn)單的4維憶阻Hopfield神經(jīng)網(wǎng)絡(luò)模型。借助理論分析和數(shù)值仿真，分析了不同憶阻突觸耦合強(qiáng)度下的復(fù)雜動(dòng)力學(xué)行為，揭示了與狀態(tài)初值密切相關(guān)的特殊動(dòng)力學(xué)行為。最后，設(shè)計(jì)了該憶阻HNN的模擬等效實(shí)現(xiàn)電路，并由PSIM電路仿真驗(yàn)證了MATLAB數(shù)值仿真的正確性。
    Abstract: The initial sensitive dynamics in a Hopfield Neural Network (HNN) with three neurons under the action of electromagnetic induction current is reported. A simple 4-D memristive HNN is constructed by using a non-ideal memristor synapse to imitate the electromagnetic induction current caused by membrane potential difference between two adjacent neurons. By means of theoretical analyses and numerical simulations, the complex dynamical behaviors under different coupling strengths of the memristor synapse are researched, and special phenomena closely related to the initial values are revealed. Finally, the analog equivalent realization circuit of the memristive HNN model is designed, and the correctness of MATLAB numerical simulation is verified by PSIM circuit simulations.
    • HTML全文

  • 圖  1  基于非理想憶阻突觸的HNN的連接拓?fù)?/p>

    圖  2  不同憶阻耦合強(qiáng)度時(shí)H1(y, z)和H2(y, z)函數(shù)曲線及交點(diǎn)平衡點(diǎn)

    圖  3  不同初值下隨參數(shù)k變化的共存分岔行為

    圖  4  不同憶阻耦合強(qiáng)度下x1–x3平面上的相軌圖

    圖  5  狀態(tài)變量x1隨狀態(tài)初值變化的分岔圖

    圖  6  不同憶阻耦合強(qiáng)度下x1(0)–x2(0)平面的吸引盆

    圖  7  不同憶阻耦合強(qiáng)度下共存吸引子在x1–x3平面的相軌圖

    圖  8  憶阻HNN模型(2)的等效實(shí)現(xiàn)電路

    圖  9  PSIM電路仿真得到的共存吸引子在v1–x3平面上的相軌圖

    表  1  k=–1, 0和1時(shí)的平衡點(diǎn)及其特征值和穩(wěn)定性

    k平衡點(diǎn)特征值穩(wěn)定性
    –1P0: (0, 0, 0, 0)1.6062, –0.9531±j2.3986, –1不穩(wěn)定指數(shù)1鞍焦
    P1: (–0.0019, –0.1689, 3.3462, 0.1670)0.0981±j2.0026, –0.8763, –0.9875不穩(wěn)定指數(shù)2鞍焦
    P2: (0.0369, 0.1814, –3.5887, –0.1445)0.5146±j2.0051, –0.9923, –1.0882不穩(wěn)定指數(shù)2鞍焦
    P3: (0.9448, 2.5018, –19.7332, –1.5570)3.4659, –0.9464, –1, –1.6894不穩(wěn)定鞍點(diǎn)
    0P0: (0, 0, 0, 0)1.6062, –0.9531±j2.3986, –1不穩(wěn)定指數(shù)1鞍焦
    P1: (0.0220, 0.1761, –3.4860, –0.1541)0.3267±j2.0074, –0.9906, –1不穩(wěn)定指數(shù)2鞍焦
    P2: (–0.0220, –0.1761, 3.4860, 0.1541)0.3267±j2.0074, –0.9906, –1不穩(wěn)定指數(shù)2鞍焦
    1P0: (0, 0, 0, 0)1.6062, –0.9531±j2.3986, –1不穩(wěn)定指數(shù)1鞍焦
    P1: (–0.9448, –2.5018, 19.7332, 1.5570)3.4659, –0.9464, –1, –1.6894不穩(wěn)定鞍點(diǎn)
    P2: (–0.0369, –0.1814, 3.5887, 0.1445)0.5146±j2.0051, –0.9923, –1.0882不穩(wěn)定指數(shù)2鞍焦
    P3: (0.0019, 0.1689, –3.3462, –0.1670)0.0981±j2.0026, –0.8763, –0.9875不穩(wěn)定指數(shù)2鞍焦
    下載: 導(dǎo)出CSV

    表  2  圖7中不同顏色吸引子對(duì)應(yīng)的初值及吸引子類型

    顏色k=0.6k=–0.5吸引子類型
    (–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)發(fā)散
    –(0, 5, 0, 0)發(fā)散
    下載: 導(dǎo)出CSV
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  • 收稿日期:  2019-11-01
  • 修回日期:  2020-01-20
  • 網(wǎng)絡(luò)出版日期:  2020-03-13
  • 刊出日期:  2020-06-04

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