簡(jiǎn)潔無(wú)電感憶阻混沌電路及其特性

曾以成; 成德武; 譚其威

doi:10.11999/JEIT190859

簡(jiǎn)潔無(wú)電感憶阻混沌電路及其特性

doi: 10.11999/JEIT190859

湘潭大學(xué)物理與光電工程學(xué)院湘潭 411105

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61471310)

詳細(xì)信息

作者簡(jiǎn)介:
曾以成：男，1962年生，教授，博士生導(dǎo)師，主要研究方向?yàn)榉蔷€(xiàn)性電路、混沌信號(hào)處理、語(yǔ)音信號(hào)處理

成德武：男，1994年生，碩士生，研究方向?yàn)榉蔷€(xiàn)性系統(tǒng)、混沌信號(hào)處理

譚其威：女，1993年生，碩士，研究方向?yàn)榉蔷€(xiàn)性系統(tǒng)、混沌信號(hào)處理

通訊作者:
曾以成　yichengz@xtu.edu.cn

中圖分類(lèi)號(hào): TN601
計(jì)量
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出版歷程
- 收稿日期: 2019-11-01
- 修回日期: 2019-11-26
- 網(wǎng)絡(luò)出版日期: 2019-12-20
- 刊出日期: 2020-06-04

A Simple Inductor-free Memristive Chaotic Circuit and Its Characteristics

School of Physics and Photoelectric Engineering, Xiangtan University, Xiangtan, 411105, China

Funds: The National Natural Science Foundation of China (61471310)

摘要

摘要: 采用非理想有源電壓控制憶阻器和磁通控制型光滑3次非線(xiàn)性憶阻器，該文設(shè)計(jì)了一種不含電感的簡(jiǎn)單(只含5個(gè)電子元器件)雙憶阻混沌電路。采用常規(guī)的非線(xiàn)性分析手段詳細(xì)研究了電路參數(shù)變化時(shí)系統(tǒng)的基本動(dòng)力學(xué)行為，例如平衡點(diǎn)穩(wěn)定性分析，相軌圖以及李雅普諾夫指數(shù)譜和分岔圖等。通過(guò)調(diào)節(jié)系統(tǒng)控制參數(shù)，該系統(tǒng)可產(chǎn)生多渦卷、多翼以及暫態(tài)混沌等十分豐富的動(dòng)力學(xué)現(xiàn)象。此外，還研究了系統(tǒng)依賴(lài)于憶阻器初始狀態(tài)的多穩(wěn)態(tài)，得到了一些有意義的結(jié)果。為驗(yàn)證電路的可行性及穩(wěn)定性，通過(guò)對(duì)憶阻器的模擬等效電路的搭建，并將該等效電路應(yīng)用于所提出的混沌電路中，硬件電路實(shí)驗(yàn)結(jié)果以及Multisim電路仿真結(jié)果與理論分析一致。
- 憶阻器 /
- 混沌電路 /
- 多穩(wěn)態(tài) /
- 暫態(tài)混沌
Abstract: A simple two-memristor chaotic circuit without inductance (only five electronic components) is designed by using a non-ideal active voltage control memristor and a flux-controlled smooth cubic nonlinear memristor. When the circuit parameters change, the basic dynamic behaviors of the system are studied in detail by the means of conventional nonlinear analysis, such as the analysis of equilibrium stability, phase diagram, Lyapunov exponent spectrum and bifurcation diagram. With the parameters changing, the proposed system can produce various phenomena of dynamics such as multi-scrolls, multi-wings and transient transition behaviors. Furthermore, the multistability characteristics of the system are also studied in the condition of changing the initial state of two memristors in system respectively, and some meaningful results are obtained. In order to verify the feasibility and stability of the circuit, the analog equivalent circuit of each memristor is constructed, and it is applied to the proposed chaotic circuit. The experimental results of the hardware circuit and the circuit simulation results of the Multisim are in good agreement with the theoretical analysis.
- Memristor /
- Chaotic circuit /
- Multistability /
- Transient transition behaviors

HTML全文

圖 1 無(wú)電感雙憶阻型混沌電路

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圖 2 憶阻器W₃等效電路

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圖 3 憶阻器W₄等效電路

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圖 4 系統(tǒng)隨c變化時(shí)李雅普諾夫指數(shù)譜和分岔圖

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圖 5 隨參數(shù)c變化的z-w相圖

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圖 6 暫態(tài)混沌現(xiàn)象

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圖 7 系統(tǒng)隨初始值w(0)變化時(shí)李雅普諾夫指數(shù)譜和分岔圖

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圖 8 憶阻器W₄隨初始值w(0)變化的x-w相圖

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圖 9 Multisim仿真電路原理圖

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圖 10 Multisim仿真結(jié)果與硬件等效電路結(jié)果比較

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表 1 憶阻器W₃隨初始狀態(tài)變化所產(chǎn)生的多穩(wěn)態(tài)舉例

z(0)取值	LE李雅普諾夫指數(shù)	系統(tǒng)狀態(tài)
4.0	(+, 0, –, –)	2翼混沌吸引子
6.5	(+, 0, –, –)	4翼混沌吸引子
13.5	(+, 0, –, –)	6翼混沌吸引子
17.5	(+, 0, –, –)	8翼混沌吸引子

下載: 導(dǎo)出CSV

表 2 簡(jiǎn)潔無(wú)電感憶阻混沌電路的參數(shù)取值

參數(shù)	名稱(chēng)	參值
$ {C_a},{C_1},{C_3}$	電容	1 nF
C₂	電容	25 nF
$ {g_a},{\rm{ }}{g_b},{\rm{ }}{g_{3,}}{g_4}$	增益	1
$ {g_1},{\rm{ }}{g_2}$	增益	0.1
R₁	電阻	0.25 kΩ
R₂	電阻	50.00 kΩ
R₃	電阻	25.00 kΩ
$ {R_4},{\rm{ }}{R_c}$	電阻	10.00 kΩ
R_b	電阻	16.70 kΩ
$ {R_d},{R_e}_,{R_5}{,}{R_6}$	電阻	2.00 kΩ

下載: 導(dǎo)出CSV

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