忆阻混沌电路的分析与实现

包伯成; 胡文; 许建平; 刘中; 邹凌

doi:10.7498/aps.60.120502

摘要

具有记忆功能的忆阻器是除电阻器、电容器和电感器之外的第四种基本二端电路元件. 提出了由-q平面上的一条三次单调上升的非线性曲线来确定的光滑磁控忆阻器,它有着斜8字形的类紧磁滞回线的伏安特性曲线. 采用此忆阻器和负电导构成的有源忆阻器替换蔡氏混沌电路中的蔡氏二极管,导出了一个基于忆阻器的混沌振荡电路. 此外,利用常规的运算放大器和乘法器等元器件给出了有源忆阻器的等效电路实现形式. 理论分析、数值仿真和电路仿真结果一致,均表明忆阻混沌电路的动力学行为依赖于忆阻器的初始状态,在不同初始状态下存在混沌振荡、周期振荡或稳定的汇等不同的运行轨道.

关键词:

Abstract

Memristor with memory function is the fourth fundamental two-terminal circuit element, besides resistor, capacitor and inductor. In this paper, a smooth flux-controlled memristor is described by a monotone-increasing nonlinearity curve in the -q plane, and it has an italic type 8 like voltage current relation curve that looks like a pinched hysteresis loop characteristics. By replacing Chua's diode with an active memristor consisting of a smooth flux-controlled memristor and a negative conductance, a memristor based chaotic oscillation is derived from Chua's circuit. Furthermore, the equivalent circuit implementation form for the active memristor is designed by utilizing conventional components such as operational amplifiers and multipliers. The results from theoretical analysis, numerical simulations and circuit simulations are completely identical with each other, and demonstrate that the dynamical behaviors of the memristor chaotic circuit are dependent on the memristor initial state, showing different orbits such as chaotic oscillation, periodic oscillation and stable sink under different initial states.

Keywords:

作者及机构信息

1.
常州大学信息科学与工程学院,常州 213164;

2.
南京航空航天大学电子信息工程学院,南京 210016;

3.
西南交通大学电气工程学院,成都 610031;

4.
南京理工大学电子工程系,南京 210094

基金项目: 国家自然科学基金(批准号:60971090)、江苏省自然科学基金(批准号:BK2009105)和航空科学基金(批准号:2009ZC52038)资助的课题.

Authors and contacts

1.
School of Information Science and Engineering, Changzhou University, Changzhou 213164, China;

2.
College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;

3.
School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China;

4.
Department of Electronic Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

参考文献

[1]	Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2]	Chua L O, Kang S M 1976 Proc. IEEE 64 209
[3]
[4]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[5]
[6]
[7]	Tour J M, He T 2008 Nature 453 42
[8]
[9]	Wey T A, Benderli S 2009 Electron. Lett. 45 1103
[10]	Witrisal K 2009 Electron. Lett. 45 713
[11]
[12]
[13]	Biolek Z, Biolek D, Biolkov V 2009 Radioengineering 18 210
[14]
[15]	Joglekar Y N, Wolf S J 2009 Eur. J. Phys. 30 661
[16]	Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[17]
[18]	Muthuswamy B 2009 IETE Techn. Rev. 26 415
[19]
[20]	Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 228
[21]
[22]	Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[23]
[24]	Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成、刘中、许建平 2010 物理学报 59 3785]
[25]
[26]	Barboza R, Chua L O 2008 Int. J. Bifur. Chaos 18 943
[27]
[28]	Bao B C, Li C B, Xu J P, Liu Z 2008 Chin. Phys. B 17 4022
[29]
[30]	Li C B, Wang D C 2009 Acta Phys. Sin. 58 764 (in Chinese) [李春彪、王德纯 2009 物理学报 58 764]
[31]
[32]
[33]	Wang X, Chen Y, Xi H, Dimitrov D 2009 IEEE Electron Device Lett. 30 294
[34]
[35]	Pershin Y V, Ventra M D 2008 Phys. Rev. B 78 113309
[36]
[37]	Zhong G 1994 IEEE Trans. Circuits Syst. 41 934
[38]
[39]	Muthuswamy B 2010 Int. J. Bifur. Chaos 20 1335

施引文献

[1]	Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2]	Chua L O, Kang S M 1976 Proc. IEEE 64 209
[3]
[4]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[5]
[6]
[7]	Tour J M, He T 2008 Nature 453 42
[8]
[9]	Wey T A, Benderli S 2009 Electron. Lett. 45 1103
[10]	Witrisal K 2009 Electron. Lett. 45 713
[11]
[12]
[13]	Biolek Z, Biolek D, Biolkov V 2009 Radioengineering 18 210
[14]
[15]	Joglekar Y N, Wolf S J 2009 Eur. J. Phys. 30 661
[16]	Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[17]
[18]	Muthuswamy B 2009 IETE Techn. Rev. 26 415
[19]
[20]	Bao B C, Liu Z, Xu J P 2010 Electron. Lett. 46 228
[21]
[22]	Bao B C, Liu Z, Xu J P 2010 Chin. Phys. B 19 030510
[23]
[24]	Bao B C, Liu Z, Xu J P 2010 Acta Phys. Sin. 59 3785 (in Chinese) [包伯成、刘中、许建平 2010 物理学报 59 3785]
[25]
[26]	Barboza R, Chua L O 2008 Int. J. Bifur. Chaos 18 943
[27]
[28]	Bao B C, Li C B, Xu J P, Liu Z 2008 Chin. Phys. B 17 4022
[29]
[30]	Li C B, Wang D C 2009 Acta Phys. Sin. 58 764 (in Chinese) [李春彪、王德纯 2009 物理学报 58 764]
[31]
[32]
[33]	Wang X, Chen Y, Xi H, Dimitrov D 2009 IEEE Electron Device Lett. 30 294
[34]
[35]	Pershin Y V, Ventra M D 2008 Phys. Rev. B 78 113309
[36]
[37]	Zhong G 1994 IEEE Trans. Circuits Syst. 41 934
[38]
[39]	Muthuswamy B 2010 Int. J. Bifur. Chaos 20 1335

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