非对称忆阻诱导的吸引子非对称演化与机理研究

武花干; 周杰; 陈胜垚; 陈墨; 徐权

doi:10.11999/JEIT210307

非对称忆阻诱导的吸引子非对称演化与机理研究

doi: 10.11999/JEIT210307

武花干¹,
周杰¹,
陈胜垚²,
陈墨¹,
徐权^1, ,

1.
常州大学微电子与控制工程学院常州 213164
2.
南京理工大学电子工程与光电技术学院南京 210094

基金项目: 国家自然科学基金(61801054, 51607013)，江苏省研究生创新项目(KYCX20_2550)

详细信息

作者简介:
武花干：女，1987年生，副教授，研究方向为非线性电路与系统、神经元功能性电路

周杰：男，1996年生，硕士生，研究方向为非线性电路与系统

陈胜垚：男，1985年生，副教授，研究方向为雷达信号处理、混沌动力学系统

陈墨：女，1982年生，副教授，研究方向为非线性电路与系统、神经元功能性电路

徐权：男，1983年生，副教授，研究方向为忆阻神经网络、非线性电路与系统

通讯作者:
徐权　xuquan@cczu.edu.cn

中图分类号: TN713; TN601
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出版历程
- 收稿日期: 2021-04-13
- 修回日期: 2021-06-30
- 网络出版日期: 2021-07-08
- 刊出日期: 2022-06-21

Asymmetric Memristor-induced Attractor Asymmetric Evolution and Its Mechanism

1.
School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
2.
School of Electronic and Optical Engineering, Nanjing University of Science & Technology, Nanjing 210094, China

Funds: The National Natural Science Foundations of China (61801054, 51607013), The Postgraduate Education Reform Projects of Jiangsu Province (KYCX20_2550)

摘要

摘要: 紧磁滞回线是评测物理器件或数学模型是否为忆阻的关键依据，其对称特性也是忆阻的重要特征之一。该文提出一种有源非对称忆阻二极管桥模拟器，它通过改变二极管桥中并联二极管的数量可实现紧磁滞回线非对称度的控制。首先，验证了该非对称忆阻模拟器的指纹特征，并着重探讨了激励频率和对称度控制参数对紧磁滞回线非对称度的影响。进一步地，将该非对称忆阻模拟器耦合到Sallen-Key高通滤波器，构建了一种无感忆阻蔡氏电路；建立了相应的无量纲系统，并揭示了系统吸引子的非对称演化现象。结合平衡点稳定性分析、分岔分析和多吸引子状态初值空间分布，阐明了吸引子非对称演化的产生机理。结果表明，受非对称忆阻的影响，无感忆阻蔡氏电路的两个不稳定鞍焦点失去平衡，导致了非对称共存分岔、多稳定模态等行为的产生。最后，由硬件电路实验验证了理论分析与数值仿真的正确性。
- 忆阻器 /
- 非对称共存分岔 /
- 多稳定模态 /
- 硬件实验
Abstract: The pinched hysteresis loop is the key basis to judge whether a physical device or a mathematical model is a memristor, and its symmetry property is also one of the important characteristics of a memristor. In this paper, an active asymmetric memristive diode-bridge emulator is proposed, whose asymmetry can be controlled by changing the number of parallel diodes in the diode-bridge. Firstly, the fingerprint of this asymmetric memristor emulator is tested, and the effects of excitation frequency and symmetry control parameter on the asymmetry of the pinched hysteresis loop are discussed. Thereafter, by coupling the asymmetric memristor into a Sallen-Key high-pass filter, an inductor-free memristive Chua’s circuit is constructed. The corresponding dimensionless system is built, upon which the asymmetric evolution feature of system attractor is uncovered. Based on the equilibrium stability analysis, bifurcation analysis and multiple attractors distribution in state initial space, the mechanism of attractor asymmetric evolution is clarified. The results demonstrated that, affected by the asymmetric memristor, two unstable saddle-foci of the inductor-free memristive Chua’s circuit are out of balance, resulting in the generations of asymmetric coexistence bifurcation and multi-stable mode. Finally, the correctness of theoretical analysis and numerical simulation are verified by hardware circuit experiment.
- Memristor /
- Asymmetric coexisting bifurcation /
- Multi-stable mode /
- Hardware experiment

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图 1 有源PAMD模拟器原理图

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图 2 紧磁滞回线数值仿真结果

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图 3 随f和m变化的紧磁滞回线非对称度演化情况

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图 4 无感忆阻蔡氏电路原理图

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图 5 系统式(7)的典型混沌吸引子

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图 6 3组不同稳定模态吸引子随m的演化情况

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图 7 由曲线交点获得的平衡点及不同m时平衡点E₂位置的演化

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图 8 与参数a₃相关的分岔图和李雅普诺夫指数谱

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图 9 不同参数m时系统式(7)的吸引盆与共存吸引子

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图 10 不同参数m时系统式(7)的共存吸引子

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图 11 硬件实验捕获的典型混沌吸引子

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图 12 实验捕获的3组不同稳定模态吸引子随m的演化情况(横轴变量均为v₃，纵轴变量均为v₁)

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表 1 m取不同值时的系统平衡点稳定性

m	平衡点	特征根	稳定性
1, 4, 8, 16	E₀ = (0, 0, 0, 0)	9.329, –1.346±28.225i, –12.000	不稳定指数1鞍焦
1, 4, 8, 16	E₁ = (–1.419, –1.419, –12.769, 0.878)	–488.920, –10.900, 1.11±27.73i	不稳定指数2鞍焦
1	E_{2, 1} = (1.419, 1.419, 12.769, 0.878)	–488.920, –10.900, 1.11±27.73i,	不稳定指数2鞍焦
4	E_{2, 4} = (1.237, 1.237, 11.133, 0.766)	–421.800, –10.890, 1.13±27.70i	不稳定指数2鞍焦
8	E_{2, 8} = (1.145, 1.145, 10.306, 0.709)	–388.170, –10.870, 1.14±27.68i	不稳定指数2鞍焦
16	E_{2, 16} = (1.052, 1.052, 9.470, 0.651)	–353.930, –10.860, 1.16±27.66i	不稳定指数2鞍焦

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