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多频激励忆阻型Shimizu-Morioka系统的簇发振荡及机理分析

李志军 方思远 周成义

引用本文: 李志军, 方思远, 周成义. 多频激励忆阻型Shimizu-Morioka系统的簇发振荡及机理分析[J]. 电子与信息学报, doi: 10.11999/JEIT190855 shu
Citation:  Zhijun LI, Siyuan FANG, Chengyi ZHOU. Bursting Oscillations and Bifurcation Mechanism in Memristor-based Shimizu–Morioka System with Multi-frequency Slow Excitations[J]. Journal of Electronics and Information Technology, doi: 10.11999/JEIT190855 shu

多频激励忆阻型Shimizu-Morioka系统的簇发振荡及机理分析

    作者简介: 李志军: 男,1973年生,教授、研究生导师,研究方向为非线性电路与系统、数模混合集成电路;
    方思远: 男,1997年生,硕士研究生,研究方向为多时间尺度非线性系统动力学;
    周成义: 男,1993年生,硕士研究生,研究方向为多时间尺度非线性系统动力学
    通讯作者: 李志军,lizhijun@xtu.edu.cn
  • 基金项目: 国家自然科学基金(61471310),国家重点研发项目(2018AAA0103300),湖南省自然科学基金(2015JJ2142)

摘要: 为了研究忆阻系统的簇发振荡及其形成机理,该文在Shimizu-Morioka(S-M)系统的基础上引入忆阻器件和两个慢变化的周期激励项,建立了一种多时间尺度的忆阻型S-M系统。首先研究了单一激励下S-M系统的簇发行为及分岔机制,得到一种对称型“sub-Hopf/sub-Hopf”簇发模式。然后借助De Moivre公式将多频激励系统转化为单频激励系统,结合快慢分析法重点分析了附加激励幅度对“sub-Hopf/sub-Hopf”簇发模式的影响。对应于不同附加激励幅度本文发现了两种新的簇发模式,即扭曲型“sub-Hopf/sub-Hopf”簇发和嵌套级联型sub-Hopf/sub-Hopf”簇发。借助时序图、分岔图和转换相图分析了相应的簇发机制。最后,采用Multisim软件搭建电路模型并进行仿真实验,得到的实验结果与理论分析结果相吻合,从而实验证明了忆阻型S-M系统的簇发模式。

English

    1. [1]

      ZHANG Zhengdi, LI Yanyan, and BI Qinsheng. Routes to bursting in a periodically driven oscillator[J]. Physics Letters A, 2013, 377(13): 975–980. doi: 10.1016/j.physleta.2013.02.022

    2. [2]

      LIEPELT S, FREUND J A, SCHIMANSKY-GEIER L, et al. Information processing in noisy burster models of sensory neurons[J]. Journal of Theoretical Biology, 2005, 237(1): 30–40. doi: 10.1016/j.jtbi.2005.03.029

    3. [3]

      BRØNS M and KAASEN R. Canards and mixed-mode oscillations in a forest pest model[J]. Theoretical Population Biology, 2010, 77(4): 238–242. doi: 10.1016/j.tpb.2010.02.003

    4. [4]

      PROSKURKIN I S and VANAG V K. New type of excitatory pulse coupling of chemical oscillators via inhibitor[J]. Physical Chemistry Chemical Physics, 2015, 17(27): 17906–17913. doi: 10.1039/C5CP02098K

    5. [5]

      HAN Xiujing, YU Yue, and ZHANG Chun. A novel route to chaotic bursting in the parametrically driven Lorenz system[J]. Nonlinear Dynamics, 2017, 88(4): 2889–2897. doi: 10.1007/s11071-017-3418-0

    6. [6]

      WU Huagan, BAO Bocheng, LIU Zhong, et al. Chaotic and periodic bursting phenomena in a memristive Wien-bridge oscillator[J]. Nonlinear Dynamics, 2016, 83(1/2): 893–903.

    7. [7]

      IZHIKEVICH E M. Neural excitability, spiking and bursting[J]. International Journal of Bifurcation and Chaos, 2000, 10(6): 1171–1266. doi: 10.1142/S0218127400000840

    8. [8]

      IZHIKEVICH E M, DESAI N S, WALCOTT E C, et al. Bursts as a unit of neural information: Selective communication via resonance[J]. Trends in Neurosciences, 2003, 26(3): 161–167. doi: 10.1016/S0166-2236(03)00034-1

    9. [9]

      INNOCENTI G, MORELLI A, GENESIO R, et al. Dynamical phases of the Hindmarsh-Rose neuronal model: Studies of the transition from bursting to spiking chaos[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007, 17(4): 043128. doi: 10.1063/1.2818153

    10. [10]

      BAO Bocheng, YANG Qinfeng, ZHU Lei, et al. Chaotic bursting dynamics and coexisting multistable firing patterns in 3D autonomous Morris-Lecar model and microcontroller-based validations[J]. International Journal of Bifurcation and Chaos, 2019, 29(10): 1950134. doi: 10.1142/S0218127419501347

    11. [11]

      LI Xianghong and HOU Jingyu. Bursting phenomenon in a piecewise mechanical system with parameter perturbation in stiffness[J]. International Journal of Non-Linear Mechanics, 2016, 81: 165–176. doi: 10.1016/j.ijnonlinmec.2016.01.014

    12. [12]

      RINZEL J. Discussion: Electrical excitability of cells, theory and experiment: Review of the Hodgkin-Huxley foundation and an update[J]. Bulletin of Mathematical Biology, 1990, 52(1/2): 5–23.

    13. [13]

      MA Xindong, CAO Shuqian. Pitchfork-bifurcation-delay-induced bursting patterns with complex structures in a parametrically driven Jerk circuit system[J]. Journal of Physics A: Mathematical and Theoretical, 2018, 51(33): 335101. doi: 10.1088/1751-8121/aace0d

    14. [14]

      TEKA W, TABAK J, and BERTRAM R. The relationship between two fast/slow analysis techniques for bursting oscillations[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2012, 22(4): 043117. doi: 10.1063/1.4766943

    15. [15]

      YU Yue, ZHANG Zhengdi, and HAN Xiujing. Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system[J]. Communications in Nonlinear Science and Numerical Simulation, 2018, 56: 380–391. doi: 10.1016/j.cnsns.2017.08.019

    16. [16]

      ZHANG Hao, CHEN Diyi, XU Beibei, et al. The slow-fast dynamical behaviors of a hydro-turbine governing system under periodic excitations[J]. Nonlinear Dynamics, 2017, 87(4): 2519–2528. doi: 10.1007/s11071-016-3208-0

    17. [17]

      HAN Xiujing, ZHANG Yi, BI Qinsheng, et al. Two novel bursting patterns in the Duffing system with multiple-frequency slow parametric excitations[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018, 28(4): 043111. doi: 10.1063/1.5012519

    18. [18]

      HAN Xiujing, YU Yue, ZHANG Chun, et al. Turnover of hysteresis determines novel bursting in Duffing system with multiple-frequency external forcings[J]. International Journal of Non-Linear Mechanics, 2017, 89: 69–74. doi: 10.1016/j.ijnonlinmec.2016.11.008

    19. [19]

      HAN Xiujing, BI Qinsheng, JI Peng, et al. Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies[J]. Physical Review E, 2015, 92(1): 012911. doi: 10.1103/PhysRevE.92.012911

    20. [20]

      WEI Mengke, HAN Xiujing, ZHANG Xiaofang, et al. Bursting oscillations induced by bistable pulse-shaped explosion in a nonlinear oscillator with multiple-frequency slow excitations[J]. Nonlinear Dynamics, 2019: 1–12. doi: 10.1007/s11071-019-05355-1

    21. [21]

      BAO Bocheng, LIU Zhong, and XU Jianping. Transient chaos in smooth memristor oscillator[J]. Chinese Physics B, 2010, 19(3): 030510. doi: 10.1088/1674-1056/19/3/030510

    22. [22]

      李志军, 曾以成. 基于文氏振荡器的忆阻混沌电路[J]. 电子与信息学报, 2014, 36(1): 88–93.
      LI Zhijun and ZENG Yicheng. A memristor chaotic circuit based on Wien-bridge oscillator[J]. Journal of Electronics &Information Technology, 2014, 36(1): 88–93.

    23. [23]

      BAO Bocheng, WU Pingye, BAO Han, et al. Chaotic bursting in memristive diode bridge-coupled Sallen-key lowpass filter[J]. Electronics Letters, 2017, 53(16): 1104–1105. doi: 10.1049/el.2017.1647

    24. [24]

      CHEN Mo, QI Jianwei, XU Quan, et al. Quasi-period, periodic bursting and bifurcations in memristor-based FitzHugh-Nagumo circuit[J]. AEU-International Journal of Electronics and Communications, 2019, 110: 152–840.

    25. [25]

      BAO Han, HU Aihuang, LIU Wenbo, et al. Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction[J]. IEEE Transactions on Neural Networks and Learning Systems, 2019. doi: 10.1109/TNNLS.2019.2905137

    26. [26]

      WU Huagan, YE Yi, CHEN Mo, et al. Extremely slow passages in low-pass filter-based memristive oscillator[J]. Nonlinear Dynamics, 2019, 97(4): 2339–2353. doi: 10.1007/s11071-019-05131-1

    27. [27]

      SHIMIZU T and MORIOKA N. On the bifurcation of a symmetric limit cycle to an asymmetric one in a simple model[J]. Physics Letters A, 1980, 76(3/4): 201–204.

    28. [28]

      FENG Wei, HE Yigang, LI Chunlai, et al. Dynamical behavior of a 3D jerk system with a generalized Memristive device[J]. Complexity, 2018, 2018: 5620956.

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  • 图 1  单激励下系统的动力学行为分析

    图 2  扭曲型“sub-Hopf/sub-Hopf”簇发振荡的时序图

    图 3  扭曲型“sub-Hopf/sub-Hopf”簇发振荡的平衡点分布曲线及和转换相图的叠加图

    图 4  级联型“sub-Hopf/sub-Hopf”簇发振荡的时序图

    图 5  级联型“sub-Hopf/sub-Hopf”簇发振荡的平衡点分布曲线及和转换相图的叠加图

    图 6  双频激励下忆阻型S-M系统的电路原理图

    图 7  扭曲型“sub-Hopf/sub-Hopf”簇发振荡的仿真结果

    图 8  嵌套级联型“sub-Hopf /sub-Hopf”簇发振荡的仿真结果

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  • 通讯作者:  李志军, lizhijun@xtu.edu.cn
  • 收稿日期:  2019-11-01
  • 录用日期:  2019-12-27
  • 网络出版日期:  2020-01-07
通讯作者: 陈斌, bchen63@163.com
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