搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一个分数阶忆阻器模型及其简单串联电路的特性

俞亚娟 王在华

引用本文:
Citation:

一个分数阶忆阻器模型及其简单串联电路的特性

俞亚娟, 王在华

A fractional-order memristor model and the fingerprint of the simple series circuits including a fractional-order memristor

Yu Ya-Juan, Wang Zai-Hua
PDF
导出引用
  • 忆阻器是具有时间记忆特性的非线性电阻. 经典HP TiO2忆阻器模型的忆阻值为此前通过忆阻器电流的时间积分, 即记忆没有损失. 而最近研究证实HP TiO2 线性忆阻器掺杂层厚度不能等于零或者器件整体厚度, 导致器件的记忆有损失. 基于此发现, 本文首先提出了一个阶数介于0 与1间的分数阶HP TiO2 线性忆阻器模型, 研究了当受到周期外激励时, 分数阶导数的阶数对其忆阻值动态范围和输出电压动态幅值的影响规律, 推导出了磁滞旁瓣面积的计算公式. 结果表明, 分数阶导数阶数对磁滞回线的形状及所围成区域面积有重要影响. 特别地, 在外激频率大于1时, 分数阶忆阻器的记忆强度达到最大. 然后讨论了此分数阶忆阻器与电容或电感串联组成的单口网络的伏安特性. 结果表明, 在周期激励驱动时, 随着分数阶导数阶数的变化, 此分数阶忆阻器与电容的串联电路呈现出纯电容电路与忆阻电路的转换, 而它与电感的串联电路则呈现出纯电感电路与忆阻电路的转换.
    A memristor is a nonlinear resistor with time memory. The resistance of a classical memristor at a given time is represented by the integration of all the full states before the time instant, a case of ideal memory without any loss. Recent studies show that there is a memory loss of the HP TiO2 linear model, in which the width of the doped layer of HP TiO2 model cannot be equal to zero or the whole width of the model. Based on this observation, a fractional-order HP TiO2 memristor model with the order between 0 and 1 is proposed, and the fingerprint analysis of the new fractional-order model under periodic external excitation is made, thus the formula for calculating the area of hysteresis loop is obtained. It is found that the shape and the area enclosed by the hysteresis loop depend on the order of the fractional-order derivative. Especially, for exciting frequency being bigger than 1, the memory strength of the memristor takes its maximal value when the order is a fractional number, not an integer. Then, the current-voltage characteristics of the simple series one-port circuit composed of the fractional-order memristor and the capacitor, or composed of the fractional-order memristor and the inductor are studied separately. Results demonstrate that at the periodic excitation, the memristor in the series circuits will have capacitive properties or inductive properties as the fractional order changes.
      通信作者: 王在华, zhwang@nuaa.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11372354)资助的课题.
      Corresponding author: Wang Zai-Hua, zhwang@nuaa.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11372354).
    [1]

    Chua L O 1971 IEEE Trans. Circ. Theory 18 507

    [2]

    Chua L O, Kang S M 1976 Proc IEEE 64 209

    [3]

    Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80

    [4]

    Williams R S 2008 IEEE Spectrum 45 24

    [5]

    Pershin Y V, Di Ventra M 2008 Phys. Rev. B 78 113309

    [6]

    Wang X B, Chen Y R, Xi H, Li H, Dimitrov D 2009 IEEE Electron Device Letters 30 294

    [7]

    Borghetti J, Li Z, Straznicky J, Li X, Ohlberg D A, Wu W, Stewart D R, Williams R S 2009 Proc Natl Acad Sci. USA 106 1699

    [8]

    Borghetti J, Snider G S, Kuekes P J, Yang J J, Stewart D R, Williams R S 2010 Nature 464 873

    [9]

    Thomas A 2013 J. Phys. D: Appl. Phys. 46 093001

    [10]

    Hu X F, Duan S K, Wang L D, Liao X F 2011 Sci. China: Informationis 41 500 (in Chinese) [胡小方, 段书凯, 王丽丹, 廖晓峰 2011 中国科学: 41 500]

    [11]

    Cai K P, Wang R, Zhou J 2010 Electronic Components and Materials 29 78 (in Chinese) [蔡坤鹏, 王睿, 周济 2010 电子元件与材料 29 78]

    [12]

    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]

    [13]

    Bao B C, Hu W, Xu J P, Liu Z, Zou L 2011 Acta Phys. Sin. 60 120502 (in Chinese) [包伯成, 胡文, 许建平, 刘中, 邹凌 2011 物理学报 60 120502]

    [14]

    Yuan F, Wang G Y, Wang X Y 2015 Chin. Phys. B 24 060506

    [15]

    Strukov D B, Williams R S 2009 Appl. Phys. A 94 515

    [16]

    Shkabko A, Aguirre M H, Marozau I, Lippert T, Weidenkaff A 2009 Appl. Phys. Lett. 95 152109

    [17]

    Muthuswamy B, Chua L O 2010 Int. J. Bifurcation and Chaos 20 1567

    [18]

    Adhikari S P, Sah M P, Kim H, Chua L O 2013 IEEE Trans. Circ. Syst. I: Regular Papers 60 3008

    [19]

    Kim H, Sah M P, Yang C J, Seongik C, Chua L O 2012 IEEE Trans. Circ. Syst. I: Regular Papers 59 2422

    [20]

    Corinto F, Ascoli A 2012 IEEE Trans. Circuits Syst. I: Regular Papers 59 2713

    [21]

    Xu M Y, Tan W C 2002 Sci. China Ser. A 32 673 (in Chinese) [徐明瑜, 谭文长 2002 中国科学 A辑 32 673]

    [22]

    Hilfer R 2000 Applications of fractional calculus in physics (Singapore: World Scientific Publishing Co Pte Ltd) 430

    [23]

    Fouda M E, Radwan A G 2013 J. Frac. Calcu. Appl. 4 1

    [24]

    Cafagna D, Grassi G 2012 Nonlinear Dyn. 70 1185

    [25]

    Sabatier J, Agrawal O P, Machado J A 2007 Advances in Fractional Calculus (Netherlands: Springer) 419

    [26]

    Podlubny I 1999 IEEE Trans. Autom. Control 44 208

    [27]

    Monje C A, Chen Y Q, Vinagre B M, Xue D Y, Feliu V 2010 Fractional-order Systems and Controls: Fundamentals and Applications(London: Springer-Verlag)

    [28]

    Podlubny I 1999 Fractional Differential Equations (SanDiego: Academic Press)

    [29]

    Rossikhin Yu A, Shitikova M V 2010 Applied Mechanics Reviews 63 010801

    [30]

    Wang Z H, Hu H Y 2009 Sci. China Ser. G 39 1495 (in Chinese) [王在华, 胡海岩 2009 中国科学 G 辑 39 1495]

    [31]

    Biolek D, Biolek Z, Biolková V 2014 Electron Lett. 50 74

    [32]

    Biolek Z, Biolek D, Biolková V 2012 IEEE Trans. Circ. Syst. II: Exp.Briefs 59 607

  • [1]

    Chua L O 1971 IEEE Trans. Circ. Theory 18 507

    [2]

    Chua L O, Kang S M 1976 Proc IEEE 64 209

    [3]

    Strukov D B, Snider G S, Stewart D R, Williams R S 2008 Nature 453 80

    [4]

    Williams R S 2008 IEEE Spectrum 45 24

    [5]

    Pershin Y V, Di Ventra M 2008 Phys. Rev. B 78 113309

    [6]

    Wang X B, Chen Y R, Xi H, Li H, Dimitrov D 2009 IEEE Electron Device Letters 30 294

    [7]

    Borghetti J, Li Z, Straznicky J, Li X, Ohlberg D A, Wu W, Stewart D R, Williams R S 2009 Proc Natl Acad Sci. USA 106 1699

    [8]

    Borghetti J, Snider G S, Kuekes P J, Yang J J, Stewart D R, Williams R S 2010 Nature 464 873

    [9]

    Thomas A 2013 J. Phys. D: Appl. Phys. 46 093001

    [10]

    Hu X F, Duan S K, Wang L D, Liao X F 2011 Sci. China: Informationis 41 500 (in Chinese) [胡小方, 段书凯, 王丽丹, 廖晓峰 2011 中国科学: 41 500]

    [11]

    Cai K P, Wang R, Zhou J 2010 Electronic Components and Materials 29 78 (in Chinese) [蔡坤鹏, 王睿, 周济 2010 电子元件与材料 29 78]

    [12]

    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]

    [13]

    Bao B C, Hu W, Xu J P, Liu Z, Zou L 2011 Acta Phys. Sin. 60 120502 (in Chinese) [包伯成, 胡文, 许建平, 刘中, 邹凌 2011 物理学报 60 120502]

    [14]

    Yuan F, Wang G Y, Wang X Y 2015 Chin. Phys. B 24 060506

    [15]

    Strukov D B, Williams R S 2009 Appl. Phys. A 94 515

    [16]

    Shkabko A, Aguirre M H, Marozau I, Lippert T, Weidenkaff A 2009 Appl. Phys. Lett. 95 152109

    [17]

    Muthuswamy B, Chua L O 2010 Int. J. Bifurcation and Chaos 20 1567

    [18]

    Adhikari S P, Sah M P, Kim H, Chua L O 2013 IEEE Trans. Circ. Syst. I: Regular Papers 60 3008

    [19]

    Kim H, Sah M P, Yang C J, Seongik C, Chua L O 2012 IEEE Trans. Circ. Syst. I: Regular Papers 59 2422

    [20]

    Corinto F, Ascoli A 2012 IEEE Trans. Circuits Syst. I: Regular Papers 59 2713

    [21]

    Xu M Y, Tan W C 2002 Sci. China Ser. A 32 673 (in Chinese) [徐明瑜, 谭文长 2002 中国科学 A辑 32 673]

    [22]

    Hilfer R 2000 Applications of fractional calculus in physics (Singapore: World Scientific Publishing Co Pte Ltd) 430

    [23]

    Fouda M E, Radwan A G 2013 J. Frac. Calcu. Appl. 4 1

    [24]

    Cafagna D, Grassi G 2012 Nonlinear Dyn. 70 1185

    [25]

    Sabatier J, Agrawal O P, Machado J A 2007 Advances in Fractional Calculus (Netherlands: Springer) 419

    [26]

    Podlubny I 1999 IEEE Trans. Autom. Control 44 208

    [27]

    Monje C A, Chen Y Q, Vinagre B M, Xue D Y, Feliu V 2010 Fractional-order Systems and Controls: Fundamentals and Applications(London: Springer-Verlag)

    [28]

    Podlubny I 1999 Fractional Differential Equations (SanDiego: Academic Press)

    [29]

    Rossikhin Yu A, Shitikova M V 2010 Applied Mechanics Reviews 63 010801

    [30]

    Wang Z H, Hu H Y 2009 Sci. China Ser. G 39 1495 (in Chinese) [王在华, 胡海岩 2009 中国科学 G 辑 39 1495]

    [31]

    Biolek D, Biolek Z, Biolková V 2014 Electron Lett. 50 74

    [32]

    Biolek Z, Biolek D, Biolková V 2012 IEEE Trans. Circ. Syst. II: Exp.Briefs 59 607

  • [1] 吴朝俊, 方礼熠, 杨宁宁. 含有偏置电压源的非齐次分数阶忆阻混沌电路动力学分析与实验研究. 物理学报, 2024, 73(1): 010501. doi: 10.7498/aps.73.20231211
    [2] 郭慧朦, 梁燕, 董玉姣, 王光义. 蔡氏结型忆阻器的简化及其神经元电路的硬件实现. 物理学报, 2023, 72(7): 070501. doi: 10.7498/aps.72.20222013
    [3] 胡炜, 廖建彬, 杜永乾. 一种适用于大规模忆阻网络的忆阻器单元解析建模策略. 物理学报, 2021, 70(17): 178505. doi: 10.7498/aps.70.20210116
    [4] 邓文, 汪礼胜, 刘嘉宁, 余雪玲, 陈凤翔. 光电协控多层MoS2记忆晶体管的阻变行为与机理研究. 物理学报, 2021, 70(21): 217302. doi: 10.7498/aps.70.20210750
    [5] 史晨阳, 闵光宗, 刘向阳. 蛋白质基忆阻器研究进展. 物理学报, 2020, 69(17): 178702. doi: 10.7498/aps.69.20200617
    [6] 徐威, 王钰琪, 李岳峰, 高斐, 张缪城, 连晓娟, 万相, 肖建, 童祎. 新型忆阻器神经形态电路的设计及其在条件反射行为中的应用. 物理学报, 2019, 68(23): 238501. doi: 10.7498/aps.68.20191023
    [7] 邵楠, 张盛兵, 邵舒渊. 具有经验学习特性的忆阻器模型分析. 物理学报, 2019, 68(19): 198502. doi: 10.7498/aps.68.20190808
    [8] 邵楠, 张盛兵, 邵舒渊. 具有感觉记忆的忆阻器模型. 物理学报, 2019, 68(1): 018501. doi: 10.7498/aps.68.20181577
    [9] 王伟, 曾以成, 孙睿婷. 含三个忆阻器的六阶混沌电路研究. 物理学报, 2017, 66(4): 040502. doi: 10.7498/aps.66.040502
    [10] 吴洁宁, 王丽丹, 段书凯. 基于忆阻器的时滞混沌系统及伪随机序列发生器. 物理学报, 2017, 66(3): 030502. doi: 10.7498/aps.66.030502
    [11] 袁泽世, 李洪涛, 朱晓华. 基于忆阻器的数模混合随机数发生器. 物理学报, 2015, 64(24): 240503. doi: 10.7498/aps.64.240503
    [12] 董哲康, 段书凯, 胡小方, 王丽丹. 两类纳米级非线性忆阻器模型及串并联研究. 物理学报, 2014, 63(12): 128502. doi: 10.7498/aps.63.128502
    [13] 刘玉东, 王连明. 基于忆阻器的spiking神经网络在图像边缘提取中的应用. 物理学报, 2014, 63(8): 080503. doi: 10.7498/aps.63.080503
    [14] 李志军, 曾以成, 李志斌. 改进型细胞神经网络实现的忆阻器混沌电路. 物理学报, 2014, 63(1): 010502. doi: 10.7498/aps.63.010502
    [15] 徐晖, 田晓波, 步凯, 李清江. 温度改变对钛氧化物忆阻器导电特性的影响. 物理学报, 2014, 63(9): 098402. doi: 10.7498/aps.63.098402
    [16] 田晓波, 徐晖, 李清江. 横截面积参数对钛氧化物忆阻器导电特性的影响. 物理学报, 2014, 63(4): 048401. doi: 10.7498/aps.63.048401
    [17] 刘东青, 程海峰, 朱玄, 王楠楠, 张朝阳. 忆阻器及其阻变机理研究进展. 物理学报, 2014, 63(18): 187301. doi: 10.7498/aps.63.187301
    [18] 许碧荣. 一种最简的并行忆阻器混沌系统. 物理学报, 2013, 62(19): 190506. doi: 10.7498/aps.62.190506
    [19] 贾林楠, 黄安平, 郑晓虎, 肖志松, 王玫. 界面效应调制忆阻器研究进展. 物理学报, 2012, 61(21): 217306. doi: 10.7498/aps.61.217306
    [20] 王羽, 欧阳洁, 杨斌鑫. 分数阶Oldroyd-B黏弹性Poiseuille流的Laplace数值反演分析. 物理学报, 2010, 59(10): 6757-6763. doi: 10.7498/aps.59.6757
计量
  • 文章访问数:  6906
  • PDF下载量:  486
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-03-28
  • 修回日期:  2015-08-22
  • 刊出日期:  2015-12-05

/

返回文章
返回