一种类Lü系统的混沌行为分析与控制  

Analysis and Control of Chaos Behavior of a Lü-like System

作　　者：孙观 崔岩[1] 何宏骏 卢晨晖 SUN Guan;CUI Yan;He Hongjun;LU Chenhui(School of Mechanical Engineering,Shanghai University of Engineering&Science,ShangHai 201620)

机构地区：[1]上海工程技术大学机械工程学院,上海201620

出　　处：《河南科技大学学报（自然科学版）》2019年第1期95-100,112,共7页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学青年基金项目(11604205)

摘　　要：提出了一种具有三维二次型的自治常微分方程组形式的类Lü系统。应用Lyapunov判定方法研究了系统平衡点的稳定性。数值仿真结果表明:该系统具有极其丰富的动力学现象。利用Routh-Hurwitz准则对受控系统进行了稳定性分析,结合线性状态反馈方法,证明了当受控系统达到控制目标时,受控系统中反馈系数的取值范围为k_1<1,k_2<-0. 5。A Lü-like system which has the form of three dimensional quadratic autonomous ordinary differential equations was proposed.Lyapunov decision method was used to study the stability of the system equilibrium point.The results of numerical simulation show that the system possesses extremely rich dynamic phenomena.The Routh-Hurwitz criterion was used to analyze the stability of the controlled system,and the linear state feedback method was combined to prove that when the system reaches the control target,the value range of feedback coefficient is k 1∈(-∞,1),k 2∈(-∞,-0.5)in the controlled system.

关 键 词：Lü系统 混沌行为 Routh-Hurwitz准则 线性状态反馈控制 稳定性 

分 类 号：O415[理学—理论物理] O322[理学—物理]