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

doi:10.11999/JEIT190858

忆阻突触耦合Hopfield神经网络的初值敏感动力学

doi: 10.11999/JEIT190858

常州大学信息科学与工程学院常州 213164

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)

详细信息

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

中图分类号: TN601; TN711.4
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出版历程
- 收稿日期: 2019-11-01
- 修回日期: 2020-01-20
- 网络出版日期: 2020-03-13
- 刊出日期: 2020-06-04

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

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。
- 非理想忆阻突触 /
- Hopfield神经网络 /
- 状态初值 /
- 数值仿真
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.
- Non-ideal memristor synapse /
- Hopfield Neural Network (HNN) /
- Initial condition /
- Numerical simulation

HTML全文

图 1 基于非理想忆阻突触的HNN的连接拓扑

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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

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图 3 不同初值下随参数k变化的共存分岔行为

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图 4 不同忆阻耦合强度下x₁–x₃平面上的相轨图

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图 5 状态变量x₁随状态初值变化的分岔图

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图 6 不同忆阻耦合强度下x₁(0)–x₂(0)平面的吸引盆

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图 7 不同忆阻耦合强度下共存吸引子在x₁–x₃平面的相轨图

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图 8 忆阻HNN模型(2)的等效实现电路

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图 9 PSIM电路仿真得到的共存吸引子在v₁–x₃平面上的相轨图

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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
–1	P₀: (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
0	P₀: (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
1	P₀: (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

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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=0.6	k=–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

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