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
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常州大學(xué)信息科學(xué)與工程學(xué)院 常州 213164
Initial Sensitive Dynamics in Memristor Synapse-coupled Hopfield Neural Network
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School of Information Science and Engineering, Changzhou University, Changzhou 213164, China
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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。
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關(guān)鍵詞:
- 非理想憶阻突觸 /
- Hopfield神經(jīng)網(wǎng)絡(luò) /
- 狀態(tài)初值 /
- 數(shù)值仿真
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. -
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 –1 P0: (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) 0 P0: (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 1 P0: (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=0.6 k=–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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