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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

李志軍, 方思遠(yuǎn), 周成義. 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[J]. 電子與信息學(xué)報(bào), 2020, 42(4): 878-887. doi: 10.11999/JEIT190855
引用本文: 李志軍, 方思遠(yuǎn), 周成義. 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[J]. 電子與信息學(xué)報(bào), 2020, 42(4): 878-887. doi: 10.11999/JEIT190855
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 & Information Technology, 2020, 42(4): 878-887. doi: 10.11999/JEIT190855
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 & Information Technology, 2020, 42(4): 878-887. 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
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

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

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

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

    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

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

    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

    圖  6  雙頻激勵(lì)下憶阻型S-M系統(tǒng)的電路原理圖

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

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

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  • 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

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