多頻激勵(lì)憶阻型Shimizu-Morioka系統(tǒng)的簇發(fā)振蕩及機(jī)理分析

李志軍; 方思遠(yuǎn); 周成義

doi:10.11999/JEIT190855

多頻激勵(lì)憶阻型Shimizu-Morioka系統(tǒng)的簇發(fā)振蕩及機(jī)理分析

doi: 10.11999/JEIT190855

湘潭大學(xué)信息工程學(xué)院湘潭 411105

基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61471310)，國(guó)家重點(diǎn)研發(fā)項(xiàng)目(2018AAA0103300)，湖南省自然科學(xué)基金(2015JJ2142)

詳細(xì)信息

作者簡(jiǎn)介:
李志軍：男，1973年生，教授、研究生導(dǎo)師，研究方向?yàn)榉蔷€性電路與系統(tǒng)、數(shù)模混合集成電路

方思遠(yuǎn)：男，1997年生，碩士生，研究方向?yàn)槎鄷r(shí)間尺度非線性系統(tǒng)動(dòng)力學(xué)

周成義：男，1993年生，碩士生，研究方向?yàn)槎鄷r(shí)間尺度非線性系統(tǒng)動(dòng)力學(xué)

通訊作者:
李志軍　lizhijun@xtu.edu.cn

中圖分類號(hào): TN601
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出版歷程
- 收稿日期: 2019-11-01
- 修回日期: 2019-12-27
- 網(wǎng)絡(luò)出版日期: 2020-01-07
- 刊出日期: 2020-06-04

Bursting Oscillations and Bifurcation Mechanism in Memristor-based Shimizu–Morioka System with Multi-frequency Slow Excitations

College of Information Engineering, Xiangtan University, Xiangtan, 411105, China

Funds: The National Natural Science Foundation of China (61471310), The National Key R&D Program of China (2018AAA0103300), The Natural Science Foundation of Hunan Province (2015JJ2142)

摘要

摘要: 為了研究憶阻系統(tǒng)的簇發(fā)振蕩及其形成機(jī)理，該文在Shimizu-Morioka(S-M)系統(tǒng)的基礎(chǔ)上引入憶阻器件和兩個(gè)慢變化的周期激勵(lì)項(xiàng)，建立了一種多時(shí)間尺度的憶阻型S-M系統(tǒng)。首先研究了單一激勵(lì)下S-M系統(tǒng)的簇發(fā)行為及分岔機(jī)制，得到一種對(duì)稱型“sub-Hopf/sub-Hopf”簇發(fā)模式。然后借助De Moivre公式將多頻激勵(lì)系統(tǒng)轉(zhuǎn)化為單頻激勵(lì)系統(tǒng)，結(jié)合快慢分析法重點(diǎn)分析了附加激勵(lì)幅度對(duì)“sub-Hopf/sub-Hopf”簇發(fā)模式的影響。對(duì)應(yīng)于不同附加激勵(lì)幅度該文發(fā)現(xiàn)了兩種新的簇發(fā)模式，即扭曲型“sub-Hopf/sub-Hopf”簇發(fā)和嵌套級(jí)聯(lián)型sub-Hopf/sub-Hopf”簇發(fā)。借助時(shí)序圖、分岔圖和轉(zhuǎn)換相圖分析了相應(yīng)的簇發(fā)機(jī)制。最后，采用Multisim軟件搭建電路模型并進(jìn)行仿真實(shí)驗(yàn)，得到的實(shí)驗(yàn)結(jié)果與理論分析結(jié)果相吻合，從而實(shí)驗(yàn)證明了憶阻型S-M系統(tǒng)的簇發(fā)模式。
- 憶阻型S-M系統(tǒng) /
- 多頻慢激勵(lì) /
- 扭曲型“sub-Hopf/sub-Hopf”簇發(fā) /
- 級(jí)聯(lián)嵌套型sub-Hopf/sub-Hopf”簇發(fā)
Abstract: In order to study the bursting oscillations and its formation mechanism of memristor-based system, a multi-timescale memristor-based S-M system is established by introducing a memristor device and two slowly changing periodic excitations into the Shimizu-Morioka (S-M) system. Firstly, the bursting behavior and bifurcation mechanism of S-M system under single excitation are studied, and a symmetric bursting pattern of “sub-Hopf/sub-Hopf” is obtained. Then the multi-frequency excitation system is transformed into single frequency excitation system by using De Moivre formula, and the influence of additional excitation amplitude and frequency on “sub Hopf / sub Hopf” bursting mode is analyzed by using the fast-slow analysis method. As a result, two new bursting patterns named as twisted “sub-Hopf/sub-Hopf” bursting and nested “sub-Hopf/sub-Hopf” are found under different amplitudes of the additional excitation. The corresponding bursting mechanisms are analyzed with time history diagram, bifurcation diagram and transformation phase diagram. Finally, Multisim simulation results, which are in good agreement with the numerical simulation results, are provided to verify the validity of the study.

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圖 1 單激勵(lì)下系統(tǒng)的動(dòng)力學(xué)行為分析

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圖 2 扭曲型“sub-Hopf/sub-Hopf”簇發(fā)振蕩的時(shí)序圖

下載: 全尺寸圖片幻燈片

圖 3 扭曲型“sub-Hopf/sub-Hopf”簇發(fā)振蕩的平衡點(diǎn)分布曲線及和轉(zhuǎn)換相圖的疊加圖

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圖 4 級(jí)聯(lián)型“sub-Hopf/sub-Hopf”簇發(fā)振蕩的時(shí)序圖

下載: 全尺寸圖片幻燈片

圖 5 級(jí)聯(lián)型“sub-Hopf/sub-Hopf”簇發(fā)振蕩的平衡點(diǎn)分布曲線及和轉(zhuǎn)換相圖的疊加圖

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圖 6 雙頻激勵(lì)下憶阻型S-M系統(tǒng)的電路原理圖

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圖 7 扭曲型“sub-Hopf/sub-Hopf”簇發(fā)振蕩的仿真結(jié)果

下載: 全尺寸圖片幻燈片

圖 8 嵌套級(jí)聯(lián)型“sub-Hopf /sub-Hopf”簇發(fā)振蕩的仿真結(jié)果

下載: 全尺寸圖片幻燈片

參考文獻(xiàn)(28)

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

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

BR?NS 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

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

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

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.

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

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

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

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

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

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.

MA Xindong, and 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

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

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

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

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

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

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

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, 2020, 99(2): 1301–1312. doi: 10.1007/s11071-019-05355-1

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

李志軍, 曾以成. 基于文氏振蕩器的憶阻混沌電路[J]. 電子與信息學(xué)報(bào), 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.

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

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: 152840.

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, 2020, 31(2): 502–511. doi: 10.1109/TNNLS.2019.2905137

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

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.

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

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