忆阻Lorenz混沌系统的动力学分析与电路实现

doi:10.19596/j.cnki.1001-246x.8649

计算物理 ›› 2024, Vol. 41 ›› Issue (2): 268-276.DOI: 10.19596/j.cnki.1001-246x.8649

• • 上一篇

忆阻Lorenz混沌系统的动力学分析与电路实现

赵双¹(), 陈湘军¹, 张云贞²^,*()

1. 常州信息职业技术学院软件与大数据学院, 江苏常州 213164
2. 许昌学院信息工程学院, 河南许昌 461000

收稿日期:2022-10-09 出版日期:2024-03-25 发布日期:2024-04-03
通讯作者: 张云贞
作者简介:赵双，女，硕士，讲师，研究方向为非线性动力学、模式识别，E-mail：zhsss1030@163.com
基金资助:
中国高校产学研创新基金(2021FNB02003);河南省高等学校重点科研项目(21A120007);河南省自然科学基金(202300410351);常州信息职业技术学院科研课题(CXZK202006Y)

Dynamics Analysis and Circuit Implementation of the Memristive Lorenz Chaotic System

Shuang ZHAO¹(), Xiangjun CHEN¹, Yunzhen ZHANG²^,*()

1. School of Software and Big Data, Changzhou College of Information Technology, Changzhou, Jiangsu 213164, China
2. School of Information Engineering, Xuchang University, Xuchang, Henan 461000, China

Received:2022-10-09 Online:2024-03-25 Published:2024-04-03
Contact: Yunzhen ZHANG

摘要/Abstract

摘要：

基于所提的一类光滑二次通用忆阻器, 构建一种忆阻Lorenz混沌系统。稳定性分析表明, 系统具有与原系统相同的平衡点和稳定性, 即一个不稳定鞍点和两个不稳定鞍焦。利用分岔图、李雅普诺夫指数谱、相图等分析方法揭示所提忆阻系统的动力学, 结果表明: 忆阻Lorenz混沌系统具有共存双稳态模式和自相似分岔结构。最后, 通过改变通用忆阻器的内部参数实现对系统的幅度调控, 分别设计忆阻器和忆阻系统等效电路并利用模拟元件综合, 仿真结果证实了数值模拟的正确性。

关键词: 通用忆阻器, 混沌动力学, Lorenz混沌系统, 双稳态, 电路实现

Abstract:

Memristor plays an important role in modeling nonlinear circuits and systems. Based on the proposed smooth quadratic generic memristor, this paper proposes a memristor-based Lorenz chaotic system. Different from the chaotic system on account of memristor feedback, this system takes a variable of the original Lorenz chaotic system as an inner state variable of memristor, so as to ensure that the system dimension does not increase. Stability analysis shows that the system has the same equilibrium point and stability as the original Lorenz system, namely, one unstable saddle point and two unstable saddle foci. By means of bifurcation diagram, Lyapunov exponent spectra, and phase plot, the dynamics of the proposed memristive system are revealed. The simulated results show that the memristive Lorenz chaotic system possesses coexisting bistable mode and self-similar bifurcation structures. What is more interesting is that the amplitude of the system can be regulated by changing the inner parameters of the generic memristor. Finally, the equivalent circuits of memristor and memristive system are designed and also synthesized by analog components. Simulation results confirm the correctness of the numerical simulations.

Key words: generic memristor, chaotic dynamics, Lorenz chaotic system, bistable mode, circuit implementation

中图分类号:

O415.5

赵双, 陈湘军, 张云贞. 忆阻Lorenz混沌系统的动力学分析与电路实现[J]. 计算物理, 2024, 41(2): 268-276.

Shuang ZHAO, Xiangjun CHEN, Yunzhen ZHANG. Dynamics Analysis and Circuit Implementation of the Memristive Lorenz Chaotic System[J]. Chinese Journal of Computational Physics, 2024, 41(2): 268-276.

图/表 8

图1 通用忆阻器的滞回曲线 (a) A=2时，f=0.1、0.5和1；(b) f=0.5时，A=1.7、2和2.3。

Fig.1 Pinched hysteresis loops of the generic memristor at (a) input voltage A=2 with frequency f=0.1, 0.5, and 1; (b) input frequency f=0.5 with voltage A=1.7, 2, and 2.3

图2 忆阻Lorenz混沌系统的相图 (a) x-y-z三维相空间；(b) x-y二维相平面; (c) x-z二维相平面；(d) y-z二维相平面

Fig.2 Phase plots of the memristive Lorenz chaotic system (a) x-y-z phase space; (b) x-y phase plane; (c) x-z phase plane; (d) y-z phase plane

图3 随参数σ变化的分岔行为 (a) 分岔图；(b) 李雅普诺夫指数谱

Fig.3 Bifurcation behaviors with the change of parameter σ (a) bifurcation diagram; (b) Lyapunov exponent spectra

图4 两类特殊的分岔行为 (a) 随参数σ变化的共存分岔；(b) 随参数b变化的自相似分岔

Fig.4 Two kinds of special bifurcation behaviors (a) coexisting bifurcation with the change of σ; (b) bifurcation behaviors with the change of parameter b

图5 共存吸引子行为 (a) σ = 2；(b) σ = 2.3；(c) σ = 2.44；(d) σ = 2.6

Fig.5 Coexisting attractor behaviors (a) σ = 2; (b) σ = 2.3; (c) σ = 2.44; (d) σ = 2.6

图6 蝴蝶状吸引子 (a) σ = 2.7，g = 1时；(b) σ = 2.7，g为不同值

Fig.6 Butterfly attractors with (a) σ = 2.7 and g = 1; (b) σ = 2.7 and different values of g

图7 (a) 忆阻器等效电路图及其滞回曲线：(b) A = 2时，F = 1 kHz、5 kHz和10 kHz；(c) F = 5 kHz时，A = 1.7 V、2 V和2.3 V

Fig.7 (a) Equivalent circuit of generic memristor and its pinched hysteresis loops: (b) input voltage A = 2 with frequency F = 1 kHz, 5 kHz, and 10 kHz; (c) input frequency F = 5 kHz with voltage A = 1.7 V, 2 V and 2.3 V

图8 (a) 系统等效电路图以及相图验证: (b) vx-vy二维相平面验证; (c) vx-vz二维相平面验证；(d) vy-vz二维相平面验证；(e) 幅度控制验证

Fig.8 (a) System equivalent circuit diagram and phase diagram verification: (b) x-y phase plane verification; (c) x-z phase plane verification; (d) y-z phase plane verification; (e) amplitude control verification

参考文献 19

1	LORENZ E N . Deterministic nonperiodic flow[J]. Journal of the Atmospheric Sciences, 1963, 20 (2): 130- 141. DOI
2	RÖSSLER O E . An equation for continuous chaos[J]. Physics Letters A, 1976, 57 (5): 397- 398. DOI
3	SPROTT J C . Some simple chaotic flows[J]. Physical Review E, 1994, 50 (2): R647- R650. DOI
4	CHEN Guanrong , UETA T . Yet another chaotic attractor[J]. International Journal of Bifurcation and Chaos, 1999, 9 (7): 1465- 1466. DOI
5	LV Jinhu , CHEN Guanrong . A new chaotic attractor coined[J]. International Journal of Bifurcation and Chaos, 2002, 12 (3): 659- 661. DOI
6	周倩, 韦笃取. 场耦合忆阻神经网络的电活动[J]. 计算物理, 2020, 37 (6): 750- 756.
7	唐利红, 贺宗梅, 姚延立. 具有隐藏超级多稳定性的磁感应HR神经元及其电路实现[J]. 计算物理, 2022, 39 (5): 589- 597.
8	XU Quan , JU Zhutao , DING Shoukui , et al. Electromagnetic induction effects on electrical activity within a memristive Wilson neuron model[J]. Cognitive Neurodynamics, 2022, 16 (5): 1221- 1231. DOI
9	罗佳, 孙亮, 乔印虎. 忆阻突触耦合环形Hopfield神经网络动力学分析及其电路实现[J]. 计算物理, 2022, 39 (1): 109- 117.
10	BAO Han , YU Xihong , XU Quan , et al. Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation[J]. Cognitive Neurodynamics, 2023, 17 (4): 1079- 1092. DOI
11	刘丽君, 韦笃取. 忆阻Rulkov神经网络同步研究[J]. 计算物理, 2023, 40 (3): 389- 400.
12	刘兴策, 刘俊俏. 五维洛伦兹型忆阻混沌系统及其电路实现[J]. 大连工业大学学报, 2022, 41 (3): 220- 227.
13	阮静雅, 孙克辉, 牟俊. 基于忆阻器反馈的Lorenz超混沌系统及其电路实现[J]. 物理学报, 2016, 65 (19): 25- 35.
14	张琳琳, 张烁. 基于Lorenz系统的忆阻混沌系统分析[J]. 电子质量, 2016, (8): 1- 5. DOI
15	HUANG Lilian , LIU Shuai , XIANG Jianhong , et al. Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors[J]. Chinese Physics B, 2021, 30 (10): 100506. DOI
16	曹可, 赖强, 赖聪. 含多吸引子的忆阻混沌系统的分析与实现[J]. 深圳大学学报(理工版), 2022, 39 (4): 480- 488.
17	秦铭宏, 赖强, 吴永红. 具有无穷共存吸引子的简单忆阻混沌系统的分析与实现[J]. 物理学报, 2022, 71 (16): 160502.
18	JIANG Yicheng , LI Chunbiao , LIU Zuohua , et al. Simplified memristive lorenz oscillator[J]. IEEE Transactions on Circuits and Systems Ⅱ-Express Briefs, 2022, 69 (7): 3344- 3348.
19	ZHANG Yunzhen , PING Yuan , ZHANG Zhili , et al. Recent advances in dimensionality reduction modeling and multistability reconstitution of memristive circuit[J]. Complexity, 2021, 2021, 2747174.

[1]	王梦蛟, 曾以成, 徐茂林. 一类自治混沌系统的动力学分析与电路实现[J]. 计算物理, 2010, 27(6): 927-932.
[2]	金明德. 非线性光学薄膜输出特性的研究[J]. 计算物理, 1995, 12(3): 330-334.

忆阻Lorenz混沌系统的动力学分析与电路实现

Dynamics Analysis and Circuit Implementation of the Memristive Lorenz Chaotic System

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 8

参考文献 19

相关文章 2

编辑推荐

Metrics

作者中心

审稿中心

期刊浏览

期刊介绍