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应用科学学报 >

2010 , Vol. 28 >Issue 4: 406 - 413

DOI: https://doi.org/10.3969/j.issn.0255-8297.2010.04.013

电子技术

四维超混沌系统及其投影同步的电路实现

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  • 1. 华南理工大学电子与信息学院，广州510641
    2. 井冈山大学数理学院，江西吉安343009
    3. 华南理工大学广州汽车学院，广州510641
刘明华，讲师，博士生，研究方向：非线性系统理论与应用，E-mail: liuminghua2000@sina.com；冯久超，教授，博导，研究方向：数字信号处理、数字通信、非线性动力学及混沌理论与应用，E-mail: fengjc@scut.edu.cn

收稿日期: 2010-05-22

  修回日期: 2010-07-09

  网络出版日期: 2010-07-23

基金资助

国家自然科学基金(No.60872123)；国家–广东省自然科学基金联合基金(No.U0835001)资助

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Circuit Design as Implementation of Four Dimensional Hyper-chaos and Its Projective Synchronization

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  • 1. School of Electronic and Information Engineering, South China University of Technology,
    Guangzhou 510641, China
    2. College of Mathematics and Physics, Jinggangshan University, Ji’an 343009, Jiangxi Province, China
    3. Guangzhou Auto College, South China University of Technology, Guangzhou 510641, China

Received date: 2010-05-22

  Revised date: 2010-07-09

  Online published: 2010-07-23

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摘要

该文基于三维混沌系统，通过引入非线性状态反馈控制器构造一个四维系统，并对四维系统的Lyapunov 指数谱、分岔图等动力学行为进行分析. 分析结果表明，四维系统具有两个正的Lyapunov指数，是一个超混沌系统. 根据线性系统稳定性理论，构造了四维超混沌系统的投影同步方案，实现同结构超混沌系统的投影同步. 在此基础上设计了四维超混沌系统的投影同步电路，由反相加法器、积分器、反相器和乘法器四部分组成. 对所设计的电路进行实验，给出的实验结果与数值仿真结果一致.

关键词： 超混沌系统; Lyapunov指数; 投影同步; 电路实验

本文引用格式

刘明华1;2， 冯久超1;3 . 四维超混沌系统及其投影同步的电路实现[J]. 应用科学学报, 2010 , 28(4) : 406 -413 . DOI: 10.3969/j.issn.0255-8297.2010.04.013

Abstract

We obtain a four-dimensional system by adding a nonlinear state feedback controller to a threedimensional chaotic system. The dynamical behaviors of this 4D system are investigated, including the Lyapunov exponent spectrum and bifurcation diagram. The results show that it is a 4D hyperchaotic system with two positive Lyapunov exponents. Projective synchronization for the 4D hyperchaotic system is realized based
on the stability criterion of linear systems. An electronic circuit is designed and implemented with projective synchronization of the 4D hyperchaotic system. The circuit consists of four parts: anti-adders, integrators, inverters and multipliers. Experimental observations are in agreement with numerical simulations.

Key words： hyperchaos; Lyapunov exponent; projective synchronization; circuit experiment

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