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基于二值和三值忆阻器模型构建的混沌系统的特性分析

王晓媛 田远泽 程知群

王晓媛, 田远泽, 程知群. 基于二值和三值忆阻器模型构建的混沌系统的特性分析[J]. 电子与信息学报, 2023, 45(12): 4556-4565. doi: 10.11999/JEIT221083
引用本文: 王晓媛, 田远泽, 程知群. 基于二值和三值忆阻器模型构建的混沌系统的特性分析[J]. 电子与信息学报, 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

基于二值和三值忆阻器模型构建的混沌系统的特性分析

doi: 10.11999/JEIT221083
基金项目: 国家自然科学基金(61871429),浙江省自然科学基金(LY18F010012),科技部基地平台项目(D20011)
详细信息
    作者简介:

    王晓媛:女,教授,研究方向为新型记忆元件(忆阻器、忆容器和忆感器)理论及应用,非线性电路系统设计和信息加密算法

    田远泽:男,硕士生,研究方向为混沌系统与图像加密算法

    程知群:男,教授,研究方向为射频集成电路设计、毫米波高速通信系统

    通讯作者:

    王晓媛 youyuan-0213@163.com

  • 中图分类号: TN918.1

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

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: 近年来,基于忆阻器的非线性动力学问题备受关注。该文以二值和三值忆阻器为例分析了二值和多值忆阻器对于混沌系统动力特性的影响。首先,将二值忆阻器引入Chen系统,构建了一个4维的基于二值忆阻器的混沌系统(BMCS)。其次,使用三值忆阻器替换上述系统中的二值忆阻器,构建一个4维的基于三值忆阻器的混沌系统(TMCS)。通过理论分析与数值仿真,从多个角度对比了两个混沌系统之间的动力学特性差异,如Lyapunov指数、分岔图、系统的平衡点、系统稳定性、对初值的敏感性以及系统的复杂度分析等。结果表明,两个基于忆阻器的混沌系统都具有无穷多个平衡点,二者产生的吸引子均为隐藏吸引子,且都存在的暂态混沌现象,但三值忆阻混沌系统具有超混沌特性,且相比二值忆阻混沌系统具有更强的初值敏感性以及更大的参数取值区间。分析得出基于三值忆阻器构建的混沌系统比基于二值忆阻器的混沌系统能够产生更为复杂的动力学特性,混沌信号也更为复杂。
  • 图  1  二值忆阻器特性曲线

    图  2  三值忆阻器特性曲线

    图  3  BMCS吸引子相图

    图  4  TMCS吸引子相图

    图  5  BMCS对应的Lyapunov指数谱

    图  6  BMCS对应的分岔图

    图  7  BMCS对应的x-z平面吸引子相图

    图  8  TMCS对应的Lyapunov指数谱

    图  9  TMCS对应的分岔图

    图  10  TMCS对应的吸引子相图

    图  11  BMCS动力学地图

    图  12  TMCS动力学地图

    图  13  BMCS暂态混沌时序图及相图

    图  14  TMCS暂态混沌时序图及相图

    图  15  TMCS超混沌时序图及相图

    图  16  BMCS的C0和SE复杂度

    图  17  TMCS的C0和SE复杂度

    表  1  混沌系统的Lyapunov指数及Lyapunov维数

    混沌系统公式LE1LE2LE3LE4DL超混沌
    BMCS式(5)2.3090–0.0017–0.0795–18.22813.1222
    TMCS式(6)2.48180.15780.0017–18.64133.1417
    下载: 导出CSV

    表  2  序列相关性的对照比较

    混沌系统X1,X2的相关性Y1,Y2的相关性Z1,Z2的相关性W1,W2的相关性
    BMCS–0.0122–0.0137–0.02070.1530
    TMCS–0.0085–0.00680.0017–0.0055
    下载: 导出CSV

    表  3  不同参数c对应的Lyapunov指数值

    参数cLE1LE2LE3LE4系统状态
    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
    下载: 导出CSV

    表  4  不同参数下TMCS对应的Lyapunov指数值

    参数cLE1LE2LE3LE4系统状态
    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
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-08-17
  • 修回日期:  2023-04-28
  • 网络出版日期:  2023-05-09
  • 刊出日期:  2023-12-26

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