一种简单并联记忆元件混沌系统的研究

doi:10.3969/j.issn.1007-5461.2021.04.014

量子电子学报 ›› 2021, Vol. 38 ›› Issue (4): 517-528.doi: 10.3969/j.issn.1007-5461.2021.04.014

一种简单并联记忆元件混沌系统的研究

李晓霞1,2∗, 王雪1,2, 冯志新1,2, 张启宇1,2, 徐桂芝1,2

( 1 河北工业大学省部共建电工装备可靠性与智能化国家重点实验室, 天津 300130; 2 河北工业大学河北省电磁场与电器可靠性重点实验室, 天津 300130 )

收稿日期:2020-03-06 修回日期:2020-04-24 出版日期:2021-07-28 发布日期:2021-07-27
通讯作者: E-mail: lixiaoxia@hebut.edu.cn
作者简介:李晓霞( 1970 - ), 女, 天津人, 博士, 副教授, 硕士生导师, 主要从事复杂网络及生物电工方面的研究。 E-mail: lixiaoxia@hebut.edu.cn
基金资助:
Supported by National Natural Science Foundation of China (国家自然科学基金, 51737003, 51977060), Natural Science Foundation of Hebei Province (河北省自然科学基金, E2011202051)

Research on a simple parallel chaotic system of memory elements

LI Xiaoxia1,2∗, WANG Xue1,2, FENG Zhixin1,2, ZHANG Qiyu1,2, XU Guizhi1,2

( 1 State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China; 2 Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China )

Received:2020-03-06 Revised:2020-04-24 Published:2021-07-28 Online:2021-07-27

摘要/Abstract

摘要： 分别设计了忆阻器、忆感器、忆容器的通用数学模型, 并以此为基础构造了简单的并联混沌系统, 分析了包括相图、时域图、Lyapunov 指数、功率谱、庞加莱截面在内的动力学特性, 证明了其超混沌特性。进一步研究了平衡点稳定性、系统参数及初始值对系统的影响, 研究结果表明: 参数的对称性变化会引起系统状态相应的对称性变化; 而在系统能混沌振荡的情况下, 初始值不影响系统的状态。最后利用 Multisim 进行了电路仿真, 数值仿真与实验结果呈现出较好的一致性, 证明该系统的现实可行性与实际存在性。该系统的研究既扩展了记忆元件在非线性范畴的应用, 又为基于记忆元件的超混沌系统的实际应用奠定了基础。

关键词: 混沌, 动力学行为, 电路实现, 记忆元件

Abstract: The universal mathematical models of memristor, meminductor and memcapacitor are de- signed respectively, and based on these models, a simple parallel chaotic system is constructed. The dynamic characteristics of the system including phase diagram, time domain diagram, Lyapunov index, power spectrum and poincare cross section are analyzed, and its hyperchaotic characteristics are proved. The influence of equilibrium point stability, system parameters and initial value on the system is further studied. And it is shown that the symmetry change of parameters will cause the corresponding symmetrychange of system state, however, the initial value does not affect the state of the system under the condition of chaotic oscillation. Finally, the circuit is designed and realized by using Multisim, and the numerical simulation results are in good agreement with the experimental results, which proves the practical feasibility and actual existence of the system. This work not only extends the application of memory element in the nonlinear category, but also makes the basic work for the practical application of memory element based hyperchaotic system.

Key words: chaos, dynamical behaviour, circuit implementation, memory element

中图分类号:

O415.5

李晓霞, ∗, 王雪, 冯志新, 张启宇, 徐桂芝, . 一种简单并联记忆元件混沌系统的研究[J]. 量子电子学报, 2021, 38(4): 517-528.

LI Xiaoxia, ∗, WANG Xue, FENG Zhixin, ZHANG Qiyu, XU Guizhi, . Research on a simple parallel chaotic system of memory elements[J]. Chinese Journal of Quantum Electronics, 2021, 38(4): 517-528.

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一种简单并联记忆元件混沌系统的研究

Research on a simple parallel chaotic system of memory elements

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