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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,  田遠澤,  程知群

王曉媛, 田遠澤, 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]. 電子與信息學報, 2023, 45(12): 4556-4565. doi: 10.11999/JEIT221083
引用本文: 王曉媛, 田遠澤, 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]. 電子與信息學報, 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 cstr: 32379.14.JEIT221083

  • 杭州電子科技大學電子信息學院 杭州 310000

基金項目: 國家自然科學基金(61871429)，浙江省自然科學基金(LY18F010012)，科技部基地平臺項目(D20011)
詳細信息
    作者簡介:

    王曉媛：女，教授，研究方向為新型記憶元件(憶阻器、憶容器和憶感器)理論及應用，非線性電路系統(tǒng)設計和信息加密算法

    田遠澤：男，碩士生，研究方向為混沌系統(tǒng)與圖像加密算法

    程知群：男，教授，研究方向為射頻集成電路設計、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: 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力學問題備受關(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于混沌系統(tǒng)動力特性的影響。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，從多個角度對比了兩個混沌系統(tǒng)之間的動力學特性差異，如Lyapunov指數(shù)、分岔圖、系統(tǒng)的平衡點、系統(tǒng)穩(wěn)定性、對初值的敏感性以及系統(tǒng)的復雜度分析等。結(jié)果表明，兩個基于憶阻器的混沌系統(tǒng)都具有無窮多個平衡點，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)生更為復雜的動力學特性，混沌信號也更為復雜。
    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.
    • HTML全文

  • 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對應的Lyapunov指數(shù)譜

    圖  6  BMCS對應的分岔圖

    圖  7  BMCS對應的x-z平面吸引子相圖

    圖  8  TMCS對應的Lyapunov指數(shù)譜

    圖  9  TMCS對應的分岔圖

    圖  10  TMCS對應的吸引子相圖

    圖  11  BMCS動力學地圖

    圖  12  TMCS動力學地圖

    圖  13  BMCS暫態(tài)混沌時序圖及相圖

    圖  14  TMCS暫態(tài)混沌時序圖及相圖

    圖  15  TMCS超混沌時序圖及相圖

    圖  16  BMCS的C0和SE復雜度

    圖  17  TMCS的C0和SE復雜度

    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: 導出CSV

    表  2  序列相關(guān)性的對照比較

    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: 導出CSV

    表  3  不同參數(shù)c對應的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: 導出CSV

    表  4  不同參數(shù)下TMCS對應的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: 導出CSV
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出版歷程
  • 收稿日期:  2022-08-17
  • 修回日期:  2023-04-28
  • 網(wǎng)絡出版日期:  2023-05-09
  • 刊出日期:  2023-12-26

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