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基于二值和三值憶阻器模型構(gòu)建的混沌系統(tǒng)的特性分析

王曉媛,  田遠(yuǎn)澤,  程知群

王曉媛, 田遠(yuǎn)澤, 程知群. 基于二值和三值憶阻器模型構(gòu)建的混沌系統(tǒng)的特性分析[J]. 電子與信息學(xué)報(bào), 2023, 45(12): 4556-4565. doi: 10.11999/JEIT221083
引用本文: 王曉媛, 田遠(yuǎn)澤, 程知群. 基于二值和三值憶阻器模型構(gòu)建的混沌系統(tǒng)的特性分析[J]. 電子與信息學(xué)報(bào), 2023, 45(12): 4556-4565. doi: 10.11999/JEIT221083
WANG Xiaoyuan, TIAN Yuanze, CHENG Zhiqun. Characteristic Analysis of Chaotic System Based on Binary-valued and Tri-valued Memristor Models[J]. Journal of Electronics & Information Technology, 2023, 45(12): 4556-4565. doi: 10.11999/JEIT221083
Citation: WANG Xiaoyuan, TIAN Yuanze, CHENG Zhiqun. Characteristic Analysis of Chaotic System Based on Binary-valued and Tri-valued Memristor Models[J]. Journal of Electronics & Information Technology, 2023, 45(12): 4556-4565. doi: 10.11999/JEIT221083

基于二值和三值憶阻器模型構(gòu)建的混沌系統(tǒng)的特性分析

doi: 10.11999/JEIT221083

  • 杭州電子科技大學(xué)電子信息學(xué)院 杭州 310000

基金項(xiàng)目: 國家自然科學(xué)基金(61871429)，浙江省自然科學(xué)基金(LY18F010012)，科技部基地平臺(tái)項(xiàng)目(D20011)
詳細(xì)信息
    作者簡(jiǎn)介:

    王曉媛：女，教授，研究方向?yàn)樾滦陀洃浽?憶阻器、憶容器和憶感器)理論及應(yīng)用，非線性電路系統(tǒng)設(shè)計(jì)和信息加密算法

    田遠(yuǎn)澤：男，碩士生，研究方向?yàn)榛煦缦到y(tǒng)與圖像加密算法

    程知群：男，教授，研究方向?yàn)樯漕l集成電路設(shè)計(jì)、毫米波高速通信系統(tǒng)

    通訊作者:

    王曉媛　youyuan-0213@163.com

  • 中圖分類號(hào): TN918.1

Characteristic Analysis of Chaotic System Based on Binary-valued and Tri-valued Memristor Models

  • School of Electronic Information, Hangzhou Dianzi University, Hangzhou 310000, China

Funds: The National Natural Science Foundation of China (61871429), The Natural Science Foundation of Zhejiang Province (LY18F010012), The Project of Ministry of Science and Technology of China (D20011)
  • 摘要: 近年來，基于憶阻器的非線性動(dòng)力學(xué)問題備受關(guān)注。該文以二值和三值憶阻器為例分析了二值和多值憶阻器對(duì)于混沌系統(tǒng)動(dòng)力特性的影響。首先，將二值憶阻器引入Chen系統(tǒng)，構(gòu)建了一個(gè)4維的基于二值憶阻器的混沌系統(tǒng)(BMCS)。其次，使用三值憶阻器替換上述系統(tǒng)中的二值憶阻器，構(gòu)建一個(gè)4維的基于三值憶阻器的混沌系統(tǒng)(TMCS)。通過理論分析與數(shù)值仿真，從多個(gè)角度對(duì)比了兩個(gè)混沌系統(tǒng)之間的動(dòng)力學(xué)特性差異，如Lyapunov指數(shù)、分岔圖、系統(tǒng)的平衡點(diǎn)、系統(tǒng)穩(wěn)定性、對(duì)初值的敏感性以及系統(tǒng)的復(fù)雜度分析等。結(jié)果表明，兩個(gè)基于憶阻器的混沌系統(tǒng)都具有無窮多個(gè)平衡點(diǎn)，二者產(chǎn)生的吸引子均為隱藏吸引子，且都存在的暫態(tài)混沌現(xiàn)象，但三值憶阻混沌系統(tǒng)具有超混沌特性，且相比二值憶阻混沌系統(tǒng)具有更強(qiáng)的初值敏感性以及更大的參數(shù)取值區(qū)間。分析得出基于三值憶阻器構(gòu)建的混沌系統(tǒng)比基于二值憶阻器的混沌系統(tǒng)能夠產(chǎn)生更為復(fù)雜的動(dòng)力學(xué)特性，混沌信號(hào)也更為復(fù)雜。
    Abstract: In recent years, nonlinear dynamics problems based on memristors have received much attention. In this paper, binary-valued and tri-valued memristors are used as examples to analyze the influence of binary-valued and multi-value memristors on the dynamic characteristics of chaotic systems. Firstly, the binary-valued memristor is introduced into the Chen system, and a four-dimensional Binary-valued Memristor-based Chaotic System(BMCS) is constructed. Secondly, a tri-valued memristor is used to replace the binary-valued memristor in the above system, and a four-dimensional Tri-valued Memristor-based Chaotic System(TMCS) is constructed. Through theoretical analysis and numerical simulation, the differences of dynamic characteristics between the two chaotic systems are compared from multiple perspectives, such as Lyapunov exponent, bifurcation diagram, equilibrium point of the system, system stability, sensitivity to initial value and system complexity analysis, etc. The results show that the two memristor-based chaotic systems have infinite equilibrium points, the attractors generated by both are hidden attractors, and both have transient chaotic phenomena, but the Tri-valued memristor chaotic system has Hyper-chaos, and has stronger initial value sensitivity than Binary-valued memristor chaotic system. Further, the Tri-valued memristor chaotic system has a larger parameter value interval than the Binary-valued memristor chaotic system to obtain chaotic sequences with sufficiently high complexity. Through analysis, it is concluded that the chaotic system based on Tri-valued memristor can generate more complex dynamic characteristics and more complex chaotic signal than the chaotic system based on binary-valued memristor.
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  • 圖  1  二值憶阻器特性曲線

    圖  2  三值憶阻器特性曲線

    圖  3  BMCS吸引子相圖

    圖  4  TMCS吸引子相圖

    圖  5  BMCS對(duì)應(yīng)的Lyapunov指數(shù)譜

    圖  6  BMCS對(duì)應(yīng)的分岔圖

    圖  7  BMCS對(duì)應(yīng)的x-z平面吸引子相圖

    圖  8  TMCS對(duì)應(yīng)的Lyapunov指數(shù)譜

    圖  9  TMCS對(duì)應(yīng)的分岔圖

    圖  10  TMCS對(duì)應(yīng)的吸引子相圖

    圖  11  BMCS動(dòng)力學(xué)地圖

    圖  12  TMCS動(dòng)力學(xué)地圖

    圖  13  BMCS暫態(tài)混沌時(shí)序圖及相圖

    圖  14  TMCS暫態(tài)混沌時(shí)序圖及相圖

    圖  15  TMCS超混沌時(shí)序圖及相圖

    圖  16  BMCS的C0和SE復(fù)雜度

    圖  17  TMCS的C0和SE復(fù)雜度

    表  1  混沌系統(tǒng)的Lyapunov指數(shù)及Lyapunov維數(shù)

    混沌系統(tǒng)公式LE1LE2LE3LE4DL超混沌
    BMCS式(5)2.3090–0.0017–0.0795–18.22813.1222否
    TMCS式(6)2.48180.15780.0017–18.64133.1417是
    下載: 導(dǎo)出CSV

    表  2  序列相關(guān)性的對(duì)照比較

    混沌系統(tǒng)X1,X2的相關(guān)性Y1,Y2的相關(guān)性Z1,Z2的相關(guān)性W1,W2的相關(guān)性
    BMCS–0.0122–0.0137–0.02070.1530
    TMCS–0.0085–0.00680.0017–0.0055
    下載: 導(dǎo)出CSV

    表  3  不同參數(shù)c對(duì)應(yīng)的Lyapunov指數(shù)值

    參數(shù)cLE1LE2LE3LE4系統(tǒng)狀態(tài)
    252.30900.0007–0.0329–23.8567混沌
    312.3090–0.0017–0.0795–18.2281混沌
    360.0068–0.0111–5.4995–5.4962周期
    下載: 導(dǎo)出CSV

    表  4  不同參數(shù)下TMCS對(duì)應(yīng)的Lyapunov指數(shù)值

    參數(shù)cLE1LE2LE3LE4系統(tǒng)狀態(tài)
    252.2273–0.0066–0.0628–18.6413混沌
    312.48180.15780.0017–18.6413超混沌
    360.0087–0.0090–5.5039–5.4958周期
    下載: 導(dǎo)出CSV
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  • 收稿日期:  2022-08-17
  • 修回日期:  2023-04-28
  • 網(wǎng)絡(luò)出版日期:  2023-05-09
  • 刊出日期:  2023-12-26

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