分数阶忆阻退化Jerk系统的特性分析与DSP实现

孙克辉; 秦川; 王会海

doi:10.11999/JEIT190904

分数阶忆阻退化Jerk系统的特性分析与DSP实现

doi: 10.11999/JEIT190904

中南大学物理与电子学院长沙 410006

详细信息

作者简介:
孙克辉：男，1968年生，教授，博士生导师，主要研究方向为混沌理论与应用、非线性电路与系统

秦川：男，1996年生，硕士生，主要研究方向为混沌动力学分析，分数阶混沌系统与应用

王会海：男，1978年生，博士，副教授，主要研究方向为混沌理论及其应用、嵌入式系统应用

通讯作者:
孙克辉　kehui@csu.edu.cn

中图分类号: TN601
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- 被引次数: 0
出版历程
- 收稿日期: 2019-11-13
- 修回日期: 2020-02-13
- 网络出版日期: 2020-03-10
- 刊出日期: 2020-06-04

Characteristics Analysis and DSP Implementation of Fractional-order Memristive Hypogenetic Jerk System

School of Physics and Electronics, Central South University, Changsha 410006, China

摘要

摘要: 为了探究分数阶形式下该类系统的动力学特性，该文将分数阶微积分引入到忆阻退化Jerk系统中，增加了一个自由度，提升了系统性能。通过相图、分岔图、李雅普诺夫指数谱、复杂度混沌图等分析了系统的动力学特性，并采用DSP技术，实现了该系统的数字电路。研究结果表明，系统拓展到分数阶后有两种不同的单涡卷吸引子，系统随初值变化呈现倍周期分岔路径，在某些特定初值处系统演化路径出现跃变。系统具有无限多个吸引子共存。
- 忆阻器 /
- 混沌 /
- 分数阶微积分 /
- 吸引子共存 /
- 多稳态
Abstract: To investigate the dynamic characteristics of this type of system in the fractional-order case, fractional-order calculus is introduced into memristive hypogenetic Jerk system, which adds one degree of freedom and improves system performance. The dynamical characteristics of the system are analyzed by phase diagram, bifurcation diagram, Lyapunov exponent spectrum, complexity chaotic diagram, etc., and the digital circuit of the system is realized by employing DSP technology. The research results show that when the system is extended to the fractional order, the system presents a period doubling bifurcation path with the initial value, and the evolution path of the system changes abruptly at some specific initial values, showing infinite coexistence of attractors.
- Memristor /
- Chaos /
- Fractional calculus /
- Coexistence attractors /
- Multistability

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图 1 系统式(1)不同平面的吸引子相图

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图 2 不同阶数下的吸引子相图

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图 3 系统阶数q变化时的动力学特性

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图 4 系统参数a变化时的动力学特性

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图 5 系统参数b变化时的动力学特性

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图 6 系统参数a-b平面SE复杂度混沌图

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图 7 系统初值y(0)变化时的动力学特性

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图 8 系统初值w(0)变化时的动力学特性

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图 9 系统初值y(0)-w(0)平面SE复杂度混沌图

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图 10 分数阶式(3)系统的多吸引子共存现象

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图 11 不同初值下系统式(1)电路实验相图

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参考文献(25)

CHUA L. Memristor-the missing circuit element[J]. IEEE Transactions on Circuit Theory, 1971, 18(5): 507–509. doi: 10.1109/TCT.1971.1083337

STRUKOV D B, SNIDER G S, STEWART D R, et al. The missing memristor found[J]. Nature, 2008, 453(7191): 80–83. doi: 10.1038/nature06932

YALAGALA B, and KHANDELWAL S. Wirelessly destructible MgO-PVP-Graphene composite based flexible transient memristor for security applications[J]. Materials Science in Semiconductor Processing, 2019, 104: 104673. doi: 10.1016/j.mssp.2019.104673

张刚, 陈和祥, 张天骐. 多用户降噪差分混沌键控通信方案[J]. 电子与信息学报, 2019, 41(2): 362–368. doi: 10.11999/JEIT171173

ZHANG Gang, CHEN Hexiang, and ZHANG Tianqi. A multiuser noise reduction differential chaos shift keying system[J]. Journal of Electronics &Information Technology, 2019, 41(2): 362–368. doi: 10.11999/JEIT171173

ZHANG Weiwei, CAO Jinde, WU Ranchao, et al. Novel results on projective synchronization of fractional-order neural networks with multiple time delays[J]. Chaos, Solitons & Fractals, 2018, 117: 76–83. doi: 10.1016/j.chaos.2018.10.009

LUNELLI L, COLLINI C, JIMENEZ-GARDUÑO A M, et al. Prototyping a memristive-based device to analyze neuronal excitability[J]. Biophysical Chemistry, 2019, 253: 106212. doi: 10.1016/j.bpc.2019.106212

闵富红, 王珠林, 王恩荣, 等. 新型忆阻器混沌电路及其在图像加密中的应用[J]. 电子与信息学报, 2016, 38(10): 2681–2688.

MIN Fuhong, WANG Zhulin, WANG Enrong, et al. New memristor chaotic circuit and its application to image encryption[J]. Journal of Electronics &Information Technology, 2016, 38(10): 2681–2688.

RAJAGOPAL K, LAAREM G, KARTHIKEYAN A, et al. Fractional order memristor no equilibrium chaotic system with its adaptive sliding mode synchronization and genetically optimized fractional order PID synchronization[J]. Complexity, 2017, 2017: 1892618. doi: 10.1155/2017/1892618

CHEN Mo, FENG Yang, BAO Han, et al. Hybrid state variable incremental integral for reconstructing extreme multistability in memristive Jerk system with cubic nonlinearity[J]. Complexity, 2019, 2019: 8549472. doi: 10.1155/2019/8549472

XU Birong, WANG Guangyi, IU H H C, et al. A memristor-meminductor-based chaotic system with abundant dynamical behaviors[J]. Nonlinear Dynamics, 2019, 96(1): 765–788. doi: 10.1007/s11071-019-04820-1

李志军, 曾以成. 基于文氏振荡器的忆阻混沌电路[J]. 电子与信息学报, 2014, 36(1): 88–93. doi: 10.3724/SP.J.1146.2013.00332

LI Zhijun and ZENG Yicheng. A memristor chaotic circuit based on Wien-bridge oscillator[J]. Journal of Electronics &Information Technology, 2014, 36(1): 88–93. doi: 10.3724/SP.J.1146.2013.00332

RAJAGOPAL K, LI Chunbiao, NAZARIMEHR F, et al. Chaotic dynamics of modified Wien bridge oscillator with fractional order memristor[J]. Radioengineering, 2019, 28(1): 165–174. doi: 10.13164/re.2019.0165

RUAN Jingya, SUN Kehui, MOU Jun, et al. Fractional-order simplest memristor-based chaotic circuit with new derivative[J]. The European Physical Journal Plus, 2018, 133(1), No.3: 1–12. doi: 10.1140/epjp/i2018-11828-0.

GUO Zhang, SI Gangquan, XU Xiang, et al. Generalized modeling and character analyzing of composite fractional-order memristors in series connection[J]. Nonlinear Dynamics, 2019, 95(1): 101–115. doi: 10.1007/s11071-018-4553-y

SI Gangquan, DIAO Lijie, and ZHU Jianwei. Fractional-order charge-controlled memristor: Theoretical analysis and simulation[J]. Nonlinear Dynamics, 2017, 87(4): 2625–2634. doi: 10.1007/s11071-016-3215-1

YANG Ningning, XU Cheng, WU Chaojun, et al. Fractional-order cubic nonlinear flux-controlled memristor: Theoretical analysis, numerical calculation and circuit simulation[J]. Nonlinear Dynamics, 2019, 97(1): 33–44. doi: 10.1007/s11071-019-04920-y

YANG Ningning, CHENG Shucan, WU Chaojun, et al. Dynamic behaviors analysis of a chaotic circuit based on a novel fractional-order generalized memristor[J]. Complexity, 2019, 2019: 6083853. doi: 10.1155/2019/6083853

MOU Jun, SUN Kehui, WANG Huihai, et al. Characteristic analysis of fractional-order 4D hyperchaotic memristive circuit[J]. Mathematical Problems in Engineering, 2017, 2017: 2313768. doi: 10.1155/2017/2313768

LI Ruihong and HUANG Dongmei. Stability analysis and synchronization application for a 4D fractional-order system with infinite equilibria[J]. Physica Scripta, 2019, 95(1): 015202. doi: 10.1088/1402-4896/ab3ed2

CHEN Chengjie, CHEN Jingqi, BAO Han, et al. Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons[J]. Nonlinear Dynamics, 2019, 95(4): 3385–3399. doi: 10.1007/s11071-019-04762-8

BAO Han, WANG Ning, BAO Bocheng, et al. Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria[J]. Communications in Nonlinear Science and Numerical Simulation, 2018, 57: 264–275. doi: 10.1016/j.cnsns.2017.10.001

WAN Peng, SUN Dihua, ZHAO Min, et al. Multistability and attraction basins of discrete-time neural networks with nonmonotonic piecewise linear activation functions[J]. Neural Networks, 2020, 122: 231–238. doi: 10.1016/j.neunet.2019.10.005

CHEN Mo, SUN Mengxia, BAO Han, et al. Flux-charge analysis of two-memristor-based Chua’s circuit: Dimensionality decreasing model for detecting extreme multistability[J]. IEEE Transactions on Industrial Electronics, 2020, 67(3): 2197–2206. doi: 10.1109/TIE.2019.2907444

贺少波, 孙克辉, 王会海. 分数阶混沌系统的Adomian分解法求解及其复杂性分析[J]. 物理学报, 2014, 63(3): 030502. doi: 10.7498/aps.63.030502

HE Shaobo, SUN Kehui, and WANG Huihai. Solution of the fractional-order chaotic system based on Adomian decomposition algorithm and its complexity analysis[J]. Acta Physica Sinica, 2014, 63(3): 030502. doi: 10.7498/aps.63.030502

孙克辉, 贺少波, 何毅, 等. 混沌伪随机序列的谱熵复杂性分析[J]. 物理学报, 2013, 62(1): 010501. doi: 10.7498/aps.62.010501

SUN Kehui, HE Shaobo, HE Yi, et al. Complexity analysis of chaotic pseudo-random sequences based on spectral entropy algorithm[J]. Acta Physica Sinica, 2013, 62(1): 010501. doi: 10.7498/aps.62.010501

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