一种忆感器模型及其振荡器的动力学特性研究

袁方; 王光义; 靳培培

doi:10.7498/aps.64.210504

摘要

忆感器是在忆阻器基础上定义的一种新型记忆电路元件. 在实际忆感器尚未实现的情况下, 为探索忆感器及其在非线性电路中的特性, 提出了一种忆感器数学模型和电路模型. 基于该模型设计了一个非线性振荡电路, 采用理论分析、仿真分析和实验验证的方法研究了忆感器模型的特性及其在电路中的动力学规律. 分岔分析表明, 在适当的参数下忆感器会使电路产生周期和混沌振荡. 设计了实现忆感器模型及其振荡器的模拟电路, 实验验证了忆感器模型和振荡器的特性, 实验结果与理论分析完全一致.

关键词:

忆感器 /
振荡器 /
混沌

Abstract

A meminductor is a new type of nonlinear inductor with memory, which is generalized from the concept of a memristor and defined by current-flux. This paper presents a flux-controlled meminductor model with a smooth quadratic function and designs its corresponding equivalent circuit, which can be used as an emulator to imitate the behavior of a meminductor when actual solid-state meminductor has not yet appeared. Furthermore, a new chaotic oscillator is designed based on this meminductor model, and the dynamical behaviors of the oscillator are investigated, such as chaotic attractors, equilibrium points, Lyapunov exponent spectrum, bifurcations and dynamical map of the system, etc. Bifurcation analysis shows that the meminductor can make the oscillator produce periodic and chaotic oscillations. Moreover, an analog circuit is designed to confirm the correction of the proposed oscillator using the proposed equivalent circuit model of meminductor. It is shown that the experimental results are in good agreement with that of the numerical simulations and the theoretical analysis.

Keywords:

meminductor /
oscillation /
chaos

作者及机构信息

1.
杭州电子科技大学射频电路与系统教育部重点实验室; 现代电路与智能信息研究所, 杭州 310018

通信作者: 王光义, wanggyi@163.com

基金项目: 国家自然科学基金(批准号: 61271064, 60971046, 61401134)、浙江省自然科学基金(批准号: LZ12F01001, LQ14F010008)和浙江省重点科技创新团队(批准号: 2010R50010)资助的课题.

Authors and contacts

1.
Key Laboratory of RF Circuits and Systems, Ministry of Education of China; Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China

Corresponding author: Wang Guang-Yi, wanggyi@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61271064, 60971046, 61401134), the Natural Science Foundations of Zhejiang Province (Grant Nos. LZ12F01001, LQ14F010008), and the Program for Zhejiang Leading Team of S&T Innovation, China (Grant No 2010R50010).

参考文献

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[9]	Yuan F, Wang G Y, Wang X Y 2015 Chin. Phys. B 24 060506
[10]	Pei J S, Wright J P, Todd M D, Masri S F, Gay-Balmaz F 2015 Nonlinear Dynamics 80 457
[11]	Fouda ME, Radwan AG 2014 Microelectron J. 45 1372
[12]	Minaei S, Goknar IC, Yildiz M, Yuce E 2015 Int. J. Electron 102 911
[13]	Pershin Y V, Di Ventra M 2010 Electron Lett. 46 517
[14]	Pershin Y V, Di Ventra M 2011 Adv. Phys. 60 145
[15]	Biolek D, Biolek Z, Biolkova V 2011 Analog Integr. Circ. S 66 129
[16]	Biolek D, Biolek Z, Biolkova V 2011 Electron Lett. 47 1385
[17]	Liang Y, Yu D S, Chen H 2013 Acta Phys. Sin. 62 158501 (in Chinese) [梁燕, 于东升, 陈昊 2013 62 158501]
[18]	Yu D S, Liang Y, Iu HHC, Chua L O 2014 IEEE T Circuits-II 61 758
[19]	Liang Y, Chen H, Yu D S 2014 IEEE T Circuits-II 61 299
[20]	Han J H, Song C, Gao S, Wang Y Y, Chen C, Pan F 2014 Acs. Nano 8 10043
[21]	Abdelouahab MS, Lozi R, Chua L 2014 Int. J. Bifurcat Chaos 24 1430023
[22]	Fouda M E., Radwan A G 2014 Circ. Syst. Signal Pr 33 1573
[23]	Sah M P, Budhathoki R K, Yang C, Kim H 2014 J. Semicond Tech. Sci. 14 750
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施引文献

[1]	Chua L O 1971 IEEE Trans. Circuit Theory 18 507
[2]	Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80
[3]	Di Ventra M, Pershin Y V, Chua L O 2009 Proc. IEEE 97 1717
[4]	Liu H J, Li Z W, Y H Q, Sun Z L, Nie H S 2014 Chin. Phys. B 23 118402
[5]	Bao B C, Hu F W, Liu Z, Xu J P 2014 Chin. Phys. B 23 070503
[6]	Liu W, Wang F Q, Ma X K 2015 Int. J. Numer Model El 28 335
[7]	Wang G Y, He J L, Yuan F, Peng C J 2013 Chin. Phys. Lett. 30 110506
[8]	Sah M P, Budhathoki R K, Yang C, Kim H 2014 Circ. Syst. Signal Pr 33 2363
[9]	Yuan F, Wang G Y, Wang X Y 2015 Chin. Phys. B 24 060506
[10]	Pei J S, Wright J P, Todd M D, Masri S F, Gay-Balmaz F 2015 Nonlinear Dynamics 80 457
[11]	Fouda ME, Radwan AG 2014 Microelectron J. 45 1372
[12]	Minaei S, Goknar IC, Yildiz M, Yuce E 2015 Int. J. Electron 102 911
[13]	Pershin Y V, Di Ventra M 2010 Electron Lett. 46 517
[14]	Pershin Y V, Di Ventra M 2011 Adv. Phys. 60 145
[15]	Biolek D, Biolek Z, Biolkova V 2011 Analog Integr. Circ. S 66 129
[16]	Biolek D, Biolek Z, Biolkova V 2011 Electron Lett. 47 1385
[17]	Liang Y, Yu D S, Chen H 2013 Acta Phys. Sin. 62 158501 (in Chinese) [梁燕, 于东升, 陈昊 2013 62 158501]
[18]	Yu D S, Liang Y, Iu HHC, Chua L O 2014 IEEE T Circuits-II 61 758
[19]	Liang Y, Chen H, Yu D S 2014 IEEE T Circuits-II 61 299
[20]	Han J H, Song C, Gao S, Wang Y Y, Chen C, Pan F 2014 Acs. Nano 8 10043
[21]	Abdelouahab MS, Lozi R, Chua L 2014 Int. J. Bifurcat Chaos 24 1430023
[22]	Fouda M E., Radwan A G 2014 Circ. Syst. Signal Pr 33 1573
[23]	Sah M P, Budhathoki R K, Yang C, Kim H 2014 J. Semicond Tech. Sci. 14 750
[24]	Yin Z Y, Tian H, Chen G H, Chua L O 2015 IEEE T Circuits-II 62 402
[25]	Bao B C, Wang C L, W G H, Q X H 2014 Acta Phys. Sin. 63 020504 (in Chinese) [包伯成, 王春丽, 武花干, 乔晓华 2014 63 020504]
[26]	Bao B C, Liu Z, Henry L 2014 Electron Lett. 50 1344

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