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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