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

基于有源广义忆阻的无感混沌电路研究

俞清 包伯成 徐权 陈墨 胡文

引用本文:
Citation:

基于有源广义忆阻的无感混沌电路研究

俞清, 包伯成, 徐权, 陈墨, 胡文

Inductorless chaotic circuit based on active generalized memristors

Yu Qing, Bao Bo-Cheng, Xu Quan, Chen Mo, Hu Wen
PDF
导出引用
  • 采用常见元器件等效实现一个广义忆阻器, 进而制作出一个电路特性可靠的非线性电路, 有助于忆阻混沌电路的非线性现象的实验展示及其所产生的混沌信号的实际工程应用. 基于忆阻二极管桥电路, 构建了一种无接地限制的、易物理实现的一阶有源广义忆阻模拟器; 由该模拟器并联电容后与RC桥式振荡器线性耦合, 实现了一种无电感元件的忆阻混沌电路; 建立了无感忆阻混沌电路的动力学模型, 开展了相应的耗散性、平衡点、稳定性和动力学行为等分析. 结果表明, 无感忆阻混沌电路在相空间中存在分布2个不稳定非零鞍焦的耗散区和包含1个不稳定原点鞍点的非耗散区; 当元件参数改变时, 无感忆阻混沌电路有着共存分岔模式和共存吸引子等非线性行为. 研制了实验电路, 该电路结构简单、易实际制作, 实验测量和数值仿真两者结果一致, 验证了理论分析的有效性.
    Equivalently implementing a generalized memristor by using common components and then making a nonlinear circuit with a reliable property, are conducive to experimentally exhibit the nonlinear phenomena of the memristive chaotic circuit and show practical applications in generating chaotic signals. Firstly, based on a memristive diode bridge circuit, a new first-order actively generalized memristor emulator is constructed with no grounded restriction and ease to realize. The mathematical model of the emulator is established and its fingerprints are analyzed by the pinched hysteresis loops with different sinusoidal voltage stimuli. The results verified by experimental measurements indicate that the emulator uses only one operational amplifier and nine elementary electronic circuit elements and is an active voltage-controlled generalized memristor. Secondly, by parallelly connecting the proposed emulator to a capacitor and then linearly coupling with an RC bridge oscillator, a memristor based chaotic circuit without any inductance element is constructed. The dynamical model of the inductorless memristive chaotic circuit is established and the phase portraits of the chaotic attractor with typical circuit parameters are obtained numerically. The dissipativity, equilibrium points, and stabilities are derived, which indicate that in the phase space of the inductorless memristive chaotic circuit there exists a dissipative area where are distributed two unstable nonzero saddle-foci and a non-dissipative area containing an unstable origin saddle point. Furthermore, by utilizing the bifurcation diagram, Lyapunov exponent spectra, and phase portraits, the dynamical behaviors of the inductorless memristive chaotic circuit are investigated. Results show that with the evolution of the parameter value of the coupling resistor, the complex nonlinear phenomena of the coexisting bifurcation modes and coexisting attractors under two different initial conditions of the state variables can be found in the inductorless memristive chaotic circuit. Finally, a prototype circuit with the same circuit parameters for numerical simulations is developed, from which it can be seen that the prototype circuit has a simple circuit structure and is inexpensive and easy to practically fabricate with common components. Results of both the experimental measurements and the numerical simulations are consistent, verifying the validity of the theoretical analyses.
      通信作者: 包伯成, mervinbao@126.com
    • 基金项目: 国家自然科学基金(批准号: 51277017)、江苏省自然科学基金(批准号: BK2012583)和南京航空航天大学基本科研业务费(批准号: NS2013025)资助的课题.
      Corresponding author: Bao Bo-Cheng, mervinbao@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No 51277017), the Natural Science Foundations of Jiangsu Province, China (Grant No BK2012583), and the NUAA Fundamental Research Funds, China (Grant No NS2013025).
    [1]

    Robinett W, Pickett M, Borghetti J, Xia Q F, Snider G S, Medeiros-Ribeiro G, Williams R S 2010 Nanotechnology 21 235203

    [2]

    Duan S K, Hu X F, Wang L D, Li C D, Mazumder P 2012 Sci. China Ser. E-Info. Sci. 42 754 (in Chinese) [段书凯, 胡小方, 王丽丹, 李传东, Mazumder P 2012 中国科学: 信息科学 42 754]

    [3]

    Vaynshteyn M, Lanis A 2013 Nat. Sci. 11 45

    [4]

    Ebong I E, Mazumder P 2012 Proc. IEEE 100 2050

    [5]

    Wu A L, Zeng Z G 2012 Neural Networks 36 1

    [6]

    Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Ser. E-Tech. Sci. 54 2180

    [7]

    Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502

    [8]

    Yu Q, Bao B C, Hu F W, Xu Q, Chen M, Wang Q 2014 Acta Phys. Sin. 63 240505 (in Chinese) [俞清, 包伯成, 胡丰伟, 徐权, 陈墨, 王将 2014 物理学报 63 240505]

    [9]

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

    [10]

    Buscarino A, Fortuna L, Frasca M, Gambuzza L V 2012 Chaos 22 023136

    [11]

    Wang G Y, He J L, Yuan F, Peng C J 2013 Chin. Phys. Lett. 30 110506

    [12]

    Li Z J, Zeng Y C 2014 J. Electron. Info. Tech. 36 88 (in Chinese) [李志军, 曾以成 2014 电子与信息学报 36 88]

    [13]

    Li Z J, Zeng Y C, Li Z B 2014 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2014 物理学报 63 010502]

    [14]

    Kim H, Sah M P, Yang C, Cho S, Chua L O 2012 IEEE Trans. Circuits Syst. I: Regular Papers 59 2422

    [15]

    Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502

    [16]

    Wu H G, Bao B C, Chen M 2014 Chin. Phys. B 23 118401

    [17]

    Wang X Y, Fitch A L, Iu H H C, Sreeramb V, Qi W G 2012 Chin. Phys. B 21 108501

    [18]

    Corinto F, Ascoli A 2012 Electron. Lett. 48 824

    [19]

    Bao B C, Yu J J, Hu F W, Liu Z 2014 Int. J. Bifur. Chaos 24 1450143

    [20]

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

    [21]

    Chua L O 2012 Proc. IEEE 100 1920

    [22]

    Banerjee T 2012 Nonlinear Dyn. 68 565

    [23]

    Gopakumar K, Premlet B, Gopchandran K G 2010 Int. J. Electronic Eng. Res. 4 489

    [24]

    Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285

    [25]

    Bilotta E丆 Pantano P, Stranges S 2007 Int. J. Bifurc. Chaos 17 1

    [26]

    Bao B C, Wang C L, Wu H G, Qiao X H 2014 Acta Phys. Sin. 63 020504 (in Chinese) [包伯成, 王春丽, 武花干, 乔晓华 2014 物理学报 63 020504]

  • [1]

    Robinett W, Pickett M, Borghetti J, Xia Q F, Snider G S, Medeiros-Ribeiro G, Williams R S 2010 Nanotechnology 21 235203

    [2]

    Duan S K, Hu X F, Wang L D, Li C D, Mazumder P 2012 Sci. China Ser. E-Info. Sci. 42 754 (in Chinese) [段书凯, 胡小方, 王丽丹, 李传东, Mazumder P 2012 中国科学: 信息科学 42 754]

    [3]

    Vaynshteyn M, Lanis A 2013 Nat. Sci. 11 45

    [4]

    Ebong I E, Mazumder P 2012 Proc. IEEE 100 2050

    [5]

    Wu A L, Zeng Z G 2012 Neural Networks 36 1

    [6]

    Bao B C, Shi G D, Xu J P, Liu Z, Pan S H 2011 Sci. China Ser. E-Tech. Sci. 54 2180

    [7]

    Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502

    [8]

    Yu Q, Bao B C, Hu F W, Xu Q, Chen M, Wang Q 2014 Acta Phys. Sin. 63 240505 (in Chinese) [俞清, 包伯成, 胡丰伟, 徐权, 陈墨, 王将 2014 物理学报 63 240505]

    [9]

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

    [10]

    Buscarino A, Fortuna L, Frasca M, Gambuzza L V 2012 Chaos 22 023136

    [11]

    Wang G Y, He J L, Yuan F, Peng C J 2013 Chin. Phys. Lett. 30 110506

    [12]

    Li Z J, Zeng Y C 2014 J. Electron. Info. Tech. 36 88 (in Chinese) [李志军, 曾以成 2014 电子与信息学报 36 88]

    [13]

    Li Z J, Zeng Y C, Li Z B 2014 Acta Phys. Sin. 63 010502 (in Chinese) [李志军, 曾以成, 李志斌 2014 物理学报 63 010502]

    [14]

    Kim H, Sah M P, Yang C, Cho S, Chua L O 2012 IEEE Trans. Circuits Syst. I: Regular Papers 59 2422

    [15]

    Bao B C, Xu J P, Zhou G H, Ma Z H, Zou L 2011 Chin. Phys. B 20 120502

    [16]

    Wu H G, Bao B C, Chen M 2014 Chin. Phys. B 23 118401

    [17]

    Wang X Y, Fitch A L, Iu H H C, Sreeramb V, Qi W G 2012 Chin. Phys. B 21 108501

    [18]

    Corinto F, Ascoli A 2012 Electron. Lett. 48 824

    [19]

    Bao B C, Yu J J, Hu F W, Liu Z 2014 Int. J. Bifur. Chaos 24 1450143

    [20]

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

    [21]

    Chua L O 2012 Proc. IEEE 100 1920

    [22]

    Banerjee T 2012 Nonlinear Dyn. 68 565

    [23]

    Gopakumar K, Premlet B, Gopchandran K G 2010 Int. J. Electronic Eng. Res. 4 489

    [24]

    Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285

    [25]

    Bilotta E丆 Pantano P, Stranges S 2007 Int. J. Bifurc. Chaos 17 1

    [26]

    Bao B C, Wang C L, Wu H G, Qiao X H 2014 Acta Phys. Sin. 63 020504 (in Chinese) [包伯成, 王春丽, 武花干, 乔晓华 2014 物理学报 63 020504]

  • [1] 王世场, 卢振洲, 梁燕, 王光义. N型局部有源忆阻器的神经形态行为. 物理学报, 2022, 71(5): 050502. doi: 10.7498/aps.71.20212017
    [2] 张柱, 吴智政, 江新祥, 王园园, 朱进利, 李峰. 磁液变形镜的镜面动力学建模和实验验证. 物理学报, 2018, 67(3): 034702. doi: 10.7498/aps.67.20171281
    [3] 李红霞, 江阳, 白光富, 单媛媛, 梁建惠, 马闯, 贾振蓉, 訾月姣. 有源环形谐振腔辅助滤波的单模光电振荡器. 物理学报, 2015, 64(4): 044202. doi: 10.7498/aps.64.044202
    [4] 钟东洲, 计永强, 邓涛, 周开利. 电光调制对外部光注入垂直腔表面发射激光器的偏振转换及其非线性动力学行为的操控性研究. 物理学报, 2015, 64(11): 114203. doi: 10.7498/aps.64.114203
    [5] 李振华, 周国华, 刘啸天, 冷敏瑞. 电感电流伪连续导电模式下Buck变换器的动力学建模与分析. 物理学报, 2015, 64(18): 180501. doi: 10.7498/aps.64.180501
    [6] 袁方, 王光义, 靳培培. 一种忆感器模型及其振荡器的动力学特性研究. 物理学报, 2015, 64(21): 210504. doi: 10.7498/aps.64.210504
    [7] 史国栋, 张海明, 包伯成, 冯霏, 董伟. 脉冲序列控制双断续导电模式BIFRED变换器的动力学建模与多周期行为. 物理学报, 2015, 64(1): 010501. doi: 10.7498/aps.64.010501
    [8] 廖志贤, 罗晓曙, 黄国现. 两级式光伏并网逆变器建模与非线性动力学行为研究. 物理学报, 2015, 64(13): 130503. doi: 10.7498/aps.64.130503
    [9] 何圣仲, 周国华, 许建平, 吴松荣, 阎铁生, 张希. 谷值V2控制Boost变换器的精确建模与动力学分析. 物理学报, 2014, 63(17): 170503. doi: 10.7498/aps.63.170503
    [10] 俞清, 包伯成, 胡丰伟, 徐权, 陈墨, 王将. 基于一阶广义忆阻器的文氏桥混沌振荡器研究. 物理学报, 2014, 63(24): 240505. doi: 10.7498/aps.63.240505
    [11] 吴松荣, 何圣仲, 许建平, 周国华, 王金平. 电压型双频率控制开关变换器的动力学建模与多周期行为分析. 物理学报, 2013, 62(21): 218403. doi: 10.7498/aps.62.218403
    [12] 沙金, 包伯成, 许建平, 高玉. 脉冲序列控制电流断续模式Buck变换器的动力学建模与边界碰撞分岔. 物理学报, 2012, 61(12): 120501. doi: 10.7498/aps.61.120501
    [13] 和兴锁, 宋明, 邓峰岩. 非惯性系下考虑剪切变形的柔性梁的动力学建模. 物理学报, 2011, 60(4): 044501. doi: 10.7498/aps.60.044501
    [14] 和兴锁, 邓峰岩, 吴根勇, 王睿. 对于具有大范围运动和非线性变形的柔性梁的有限元动力学建模. 物理学报, 2010, 59(1): 25-29. doi: 10.7498/aps.59.25
    [15] 邹建龙, 马西奎. 级联功率因数校正变换器的级间耦合非线性动力学行为分析. 物理学报, 2010, 59(6): 3794-3801. doi: 10.7498/aps.59.3794
    [16] 包伯成, 周国华, 许建平, 刘中. 斜坡补偿电流模式控制开关变换器的动力学建模与分析. 物理学报, 2010, 59(6): 3769-3777. doi: 10.7498/aps.59.3769
    [17] 和兴锁, 邓峰岩, 王睿. 具有大范围运动和非线性变形的空间柔性梁的精确动力学建模. 物理学报, 2010, 59(3): 1428-1436. doi: 10.7498/aps.59.1428
    [18] 包伯成, 刘中, 许建平. 忆阻混沌振荡器的动力学分析. 物理学报, 2010, 59(6): 3785-3793. doi: 10.7498/aps.59.3785
    [19] 彭建华, 熙莹, 田小健. 含有源非线性负阻二端网络电路系统的动力学行为. 物理学报, 1992, 41(2): 193-200. doi: 10.7498/aps.41.193
    [20] 郭世宠, 蔡诗东. 阈值附近撕裂模的非线性行为. 物理学报, 1984, 33(6): 861-866. doi: 10.7498/aps.33.861
计量
  • 文章访问数:  5105
  • PDF下载量:  449
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-01-22
  • 修回日期:  2015-04-26
  • 刊出日期:  2015-09-05

/

返回文章
返回