一类超混沌系统的动力学分析及电路实现  

Dynamic Analysis and Circuit Realization of a New Hyperchaotic System

作　　者：宋爽 汤琼[1] 瞿民凯 赵思远 SONG Shuang;TANG Qiong;QU Minkai;ZHAO Siyuan(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2021年第6期33-40,共8页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(11975094);湖南省自然科学基金资助项目(2018JJ4062);湖南省科技厅青年基金资助项目(2018JJ3112)。

摘　　要：为实现混沌系统电路,在三维Lü系统的基础上,采用状态变量反馈法构造了一个基于状态变量反馈的新四维动力学超混沌系统,并且对该系统进行了基本的动力学分析。即通过根据平衡点对应的雅可比矩阵计算出相应的特征值判定平衡点的稳定性,利用相空间容积率研究系统的耗散性等方法对系统进行了定性分析;并通过计算Lyapunov指数和维数、绘制Poincaré截面图等,对系统进行了数值仿真定量分析。最后,通过基本的运算放大电路,搭建了新超混沌系统的电路模型,并利用Matlab-Simulink验证了电路实现的准确性。In view of the realization of a chaotic system circuit,based on the three-dimensional Lüsystem,a new four-dimensional dynamic hyperchaotic system,with the state variable feedback incorporated,has thus been constructed by adopting the state variable feedback method,followed by a basic dynamic analysis to be carried out.That is,the stability of the equilibrium point is judged by calculating the corresponding eigenvalues according to the Jacobian matrix in consistence with the equilibrium point,with a qualitative analysis to be carried out by using the method of phase space volume ratio to study the dissipation of the system;by calculating the Lyapunov exponent and dimension,and drawing a Poincarécross-section diagram,etc.,a numerical simulation and quantitative analysis of the system are to be carried out as well.Finally,the circuit model of the new hyperchaotic system is built through the basic operational amplifier circuit,thus verifying the accuracy of the circuit realization by Matlab-Simulink.

关 键 词：超混沌系统 动力学特性 运算放大电路 电路实现 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]