切换忆阻神经网络的建模、动力学分析与实现

doi:10.16182/j.issn1004731x.joss.25-1025

摘要/Abstract

摘要：

为模拟生物大脑神经网络的动态功能切换机制，提出了四维时序切换忆阻Hopfield神经网络(time-switched memristive Hopfield neural network, TSM-HNN)模型。该模型以标准Hopfield神经网络为基础，引入并联忆阻器作为突触，并构建了其数学模型。通过外部时序信号的选择性激活，模型能够在不改变拓扑结构的前提下，实现对系统非线性动力学特性的动态调控。TSM-HNN单一系统在连续演化过程中，能生成数量和形态均不相同的多涡卷混沌吸引子，突破了传统混沌系统只能产生单一类型吸引子的局限。研究揭示了系统复杂的混沌行为、对初始条件的高度敏感性，并发现了由初始偏移增强的共存吸引子及同质多稳定性。通过PSPice平台进行了硬件电路设计与仿真，实验结果验证了所提模型的物理可行性。研究表明，忆阻突触的时序切换能够有效增强系统的随机性与复杂性，该模型在混沌加密与安全通信等领域具备潜在的应用价值。

关键词: 忆阻器, Hopfield神经网络, 时序切换, 多涡卷混沌吸引子, 多稳态性

Abstract:

To simulate the dynamic functional switching of brain networks, a time-switched memristive Hopfield neural network (TSM-HNN) model is proposed. The model utilizes external time-sequential signals to control memristive synapses, allowing it to dynamically generate multi-scroll chaotic attractors of varying numbers and morphologies without altering the system's structure. This overcomes the limitation of traditional chaotic systems, which can typically only produce a single type of attractor. The model exhibits complex chaotic behavior, high sensitivity to initial conditions, and coexisting attractors. Its physical feasibility has been verified through PSPice circuit simulations. This enhanced complexity and randomness give the model significant potential for applications in fields such as chaotic encryption and secure communication.

Key words: memristor, Hopfield neural network, time-switched, multi-scroll chaotic attractor, multistability

中图分类号:

TP391.9

瞿壮,张绍华,王聪等 . 切换忆阻神经网络的建模、动力学分析与实现[J]. 系统仿真学报, 2026, 38(9): 2590-2606.

Qu Zhuang,Zhang Shaohua,Wang Cong,et al . Modeling, Dynamical Analysis, and lmplementation of switched Memristive Neural Networks[J]. Journal of System Simulation, 2026, 38(9): 2590-2606.

图/表 23

图1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

图15

图16

图17

图18

图19

图20

图21

图22

图23

参考文献 34

[1]	Ma Jun, Tang Jun. A Review for Dynamics in Neuron and Neuronal Network[J]. Nonlinear Dynamics, 2017, 89(3): 1569-1578.
[2]	Xu Quan, Wang Kai, Feng Chengtao, et al. Dynamical Effects of Low-frequency and High-frequency Current Stimuli in a Memristive Morris-lecar Neuron Model[J]. Chaos Solitons & Fractals, 2024, 189: 115646.
[3]	Erkan Erdem, Erkan Yasemin. Chaos-driven Dynamics in Morris-lecar Neurons: Implications for Real-world Classification[J]. Physica A: Statistical Mechanics and its Applications, 2025, 675: 130790.
[4]	Hodgkin A L, Huxley A F. A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve[J]. The Journal of Physiology, 1952, 117(4): 500-544.
[5]	Hopfield J J. Neural Networks and Physical Systems with Emergent Collective Computational Abilities[J]. Proceedings of the National Academy of Sciences of the United States of America, 1982, 79(8): 2554-2558.
[6]	Lu Jiakai, Min Fuhong, Gan Linghu, et al. Dynamic Analysis of Coupled Hindmarsh-rose Neurons with Enhanced FPGA Implementation[J]. Chaos Solitons & Fractals, 2025, 191: 115889.
[7]	Durairaj Premraj, Kanagaraj Sathiyadevi, Guo Yingshan, et al. Explosive Transitions in Aging Dynamics of Coupled Hindmarsh-rose Neurons with Distance-dependent Interactions[J]. Chaos Solitons & Fractals, 2025, 198: 116542.
[8]	Bashkirtseva I, Ryashko L. Dynamical Variability, Order-chaos Transitions, and Bursting Canards in the Memristive Rulkov Neuron Model[J]. Chaos Solitons & Fractals, 2024, 186: 115317.
[9]	Li Gaolei, Duan Jicheng, Yue Zhixuan, et al. Dynamical Analysis of the Rulkov Model with Quasiperiodic Forcing[J]. Chaos Solitons & Fractals, 2024, 189: 115605.
[10]	温新宇, 王亚赛, 何毓辉, 等. 忆阻类脑计算[J]. 物理学报, 2022, 71(14): 1-25.
	Wen Xinyu, Wang Yasai, He Yuhui, et al. Memristive Brain-like Computing[J]. Acta Physica Sinica, 2022, 71(14): 1-25 (in Chinese).
[11]	贡以纯, 明建宇, 吴思齐, 等. 面向类脑计算的低电压忆阻器研究进展[J]. 物理学报, 2024, 73(20): 227-251.
	Gong Yichun, Ming Jianyu, Wu Siqi, et al. Recent Progress of Low-voltage Memristor for Neuromorphic Computing[J]. Acta Physica Sinica, 2024, 73(20): 227-251 (in Chinese).
[12]	You Qi, Huang Fu, Fang Feier, et al. Controllable Volatile-to-nonvolatile Memristive Switching in Single-crystal Lead-free Double Perovskite with Ultralow Switching Electric Field[J]. Science China Materials, 2023, 66(1): 241-248.
[13]	Duan Zhikui, Zhang Xin, He Shaobo, et al. Implementation of a Fully Integrated Memristive Chua's Chaotic Circuit with a Voltage-controlled Oscillator[J]. Integration, 2024, 99: 102258.
[14]	Lin Mi, Luo Wenyao, Han Qi, et al. Testability Design of Memristive Digital Circuits Based on Knowm Memristor[J]. Microelectronics Reliability, 2023, 146: 115009.
[15]	Akshay Kumar Maan, Deepthi Anirudhan Jayadevi, Alex Pappachen James. A Survey of Memristive Threshold Logic Circuits[J]. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(8): 1734-1746.
[16]	Deng Quanli, Wang Chunhua, Lin Hairong. Memristive Hopfield Neural Network Dynamics with Heterogeneous Activation Functions and Its Application[J]. Chaos Solitons & Fractals, 2024, 178: 114387.
[17]	Lai Qiang, Lai Cong, Paul Didier Kamdem Kuate, et al. Chaos in a Simplest Cyclic Memristive Neural Network[J]. International Journal of Bifurcation and Chaos, 2022, 32(3): 2250042.
[18]	王梦蛟, 杨琛, 贺少波, 等. 一种新型复合指数型局部有源忆阻器耦合的Hopfield神经网络[J]. 物理学报, 2024, 73(13): 52-63.
	Wang Mengjiao, Yang Chen, He Shaobo, et al. A Novel Compound Exponential Locally Active Memristor Coupled Hopfield Neural Network[J]. Acta Physica Sinica, 2024, 73(13): 52-63.
[19]	Sun Junwei, Li Chuangchuang, Wang Zicheng, et al. Dynamic Analysis of HR-FN-HR Neural Network Coupled by Locally Active Hyperbolic Memristors and Encryption Application Based on Knuth-durstenfeld Algorithm[J]. Applied Mathematical Modelling, 2023, 121: 463-483.
[20]	Vignesh D, Ma Jun, Banerjee Santo. Multi-scroll and Coexisting Attractors in a Hopfield Neural Network Under Electromagnetic Induction and External Stimuli[J]. Neurocomputing, 2024, 564: 126961.
[21]	Luo Min, Wang Pingli, Qiu Da, et al. Analysis and Application of Conditionally Symmetric Memristive Chaotic Systems with Attractor Growth Phenomena[J]. Chaos Solitons & Fractals, 2025, 200, Part 2: 117027.
[22]	Hu Xiaoyu, Wang Siteng, Wu Panpan, et al. Self-excited and Hidden Multi-scroll Attractors in a Novel Extremely Simple Three-dimensional System[J]. Chinese Journal of Physics, 2025, 96: 826-839.
[23]	徐昌彪, 黎金龙, 许浩南. 一种基于Logistic电平脉冲的多涡卷系统及其图像加密应用[J]. 电子与信息学报, 2022, 44(12): 4328-4336.
	Xu Changbiao, Li Jinlong, Xu Haonan. A Multi-scroll System and Its Application for Image Encryption Based on Logistic Level Pulse[J]. Journal of Electronics & Information Technology, 2022, 44(12): 4328-4336 (in Chinese).
[24]	Zainab Dheyaa Ridha, Shukur Ali. The Braids: Coexistence of Attractors in Multi-scroll Chaotic System with Periodically Forced Term[J]. Chaos Solitons & Fractals, 2025, 199, Part 2: 116777.
[25]	Wan Qiuzhen, Yan Zidie, Li Fei, et al. Multistable Dynamics in a Hopfield Neural Network Under Electromagnetic Radiation and Dual Bias Currents[J]. Nonlinear Dynamics, 2022, 109(3): 2085-2101.
[26]	Yu Fei, Yu Qiulin, Chen Huifeng, et al. Dynamic Analysis and Audio Encryption Application in IoT of a Multi-scroll Fractional-order Memristive Hopfield Neural Network[J]. Fractal and Fractional, 2022, 6(7): 370.
[27]	Zhang Sen, Li Yongxin, Wang Xiaoping, et al. Initial Offset-boosted Coexisting Hidden Chaos and Firing Multistability in Memristive Ring Neural Network with Hardware Implementation[J]. IEEE Transactions on Industrial Electronics, 2025, 72(2): 2024-2033.
[28]	Wan Qiuzhen, Yan Zidie, Li Fei, et al. Complex Dynamics in a Hopfield Neural Network Under Electromagnetic Induction and Electromagnetic Radiation[J]. Chaos, 2022, 32(7): 073107.
[29]	Zhang Shaohua, Wang Cong, Zhang Hongli, et al. Collective Dynamics of Adaptive Memristor Synapse-cascaded Neural Networks Based on Energy Flow[J]. Chaos, Solitons & Fractals, 2024, 186: 115191.
[30]	Fiona E Müllner, Roska Botond. Individual Thalamic Inhibitory Interneurons are Functionally Specialized Toward Distinct Visual Features[J]. Neuron, 2024, 112(16): 2765-2782.e9.
[31]	Chua L. Everything You Wish to Know About Memristors but are Afraid to Ask[M]. Cham: Springer International Publishing, 2019: 89-157.
[32]	Lin Hairong, Wang Chunhua, Sun Yichuang. A Universal Variable Extension Method for Designing Multiscroll/Wing Chaotic Systems[J]. IEEE Transactions on Industrial Electronics, 2024, 71(7): 7806-7818.
[33]	Hassan Saberi Nik, Effati Sohrab, Saberi-Nadjafi Jafar. Ultimate Bound sets of a Hyperchaotic System and Its Application in Chaos Synchronization[J]. Complexity, 2015, 20(4): 30-44.
[34]	Zhou Ping, Hu Xikui, Zhu Zhigang, et al. What is the Most Suitable Lyapunov Function?[J]. Chaos Solitons & Fractals, 2021, 150: 111154.