五维系统的混沌动力学分析  

Analysis of chaotic dynamics of five-dimensional system

作　　者：王鹍[1,2] 刘亚秋[2] 郝兵[1] 史庆武[1] 

机构地区：[1]佳木斯大学信息电子技术学院,黑龙江佳木斯154007 [2]东北林业大学信息与计算机工程学院,哈尔滨150040

出　　处：《沈阳师范大学学报（自然科学版）》2015年第1期76-80,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(31370565);佳木斯大学面上科研项目(L2010-128);黑龙江省自然科学基金资助项目(E201212);黑龙江省教育厅科研面上项目(12521539)

摘　　要：以一个五维混沌系统为研究对象,利用状态变量反馈方法,引入一个线性控制器,形成一个五维受控系统。利用李雅普诺夫方法和劳斯稳定判据进行理论分析,设计控制器,求出受控系统渐近稳定的控制律。采用数值仿真试验的方法进一步研究该五维受控系统的动力学行为及其混沌运动特征。线性控制器在不同的参数区域内选取控制参数,该五维受控系统的响应曲线呈现出平衡点渐近稳定、收敛到某些固定点、周期轨道运动、新混沌的分岔现象。提供了一个动力学性态丰富的五维混沌控制和反控制系统。对需求高维混沌信号的混沌保密通信等相关领域提供了理论和试验支持。A 5-dimensional chaos system is taken as the object of this paper. A linear controller is introduced by thestate variables feedback method to form a 5-dimensional controlled system. The Lyapunov method and the Routh criterionare used for theoretical analysis and controller design, and then a control law of asymptotical stable controlled system isobtained. The dynamic behavior and its chaos motion characteristics of this 5-dimensional controlled system are furtherstudied by the numerical simulation method. Given linear controller with the control parameters selected in differentregions, the response curves of this 5-dimensional controlled system show the bifurcations such as asymptotic stability atthe equilibrium point, convergence at some fixed points, periodic orbit motion, new chaos, etc. A rich characteristicdynamic 5-dimensional chaos control and anti-control system is proposed here, providing theoretcial and experimentalsupport for the related fields of chaos secure communication, which require high-dimensional chaos signals.

关 键 词：五维混沌系统 动力学分析 混沌控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]