Lorenz系统族的混沌控制研究  

Study on Control of Chaotic Lorenz System Family

作　　者：解霞[1] 李烁一[1] 卢志强[1] 

机构地区：[1]南通大学,江苏南通226007

出　　处：《南通大学学报（自然科学版）》2008年第4期73-77,共5页Journal of Nantong University(Natural Science Edition)　

摘　　要：利用自反馈控制、外场控制、错位反馈控制等方法控制洛伦兹系统族,使其由混沌态稳定到周期态或稳态.利用Matlab软件分别研究最大lyapunov指数与2个可变参量k及α的关系,确定能够抑制混沌的反馈系数或反馈外场的取值范围,同时通过相图说明受控系统的动力学特性.计算结果表明:自反馈控制所需的反馈系数最小;外场控制的受控系统对初始条件的敏感使得控制过程中需加入较强的外场;而错位反馈控制法仅对广义Lorenz系统和广义Chen系统有效.We investigate the methods of a self-feedback control, an injected field control and a mismatch-feedback control. All these three methods can control the chaotic Lorenz system family to a periodic state or a fixed point. The classical lyapunov exponent method is a useful numerical tool in finding chaos. We use the Matlab software to calculate the numerical solution and analyze the dynamics of the controlled systems by the phase diagram. As a result, we find the parameter regions of feedback control which can inhibit the chaos in the Lorenz system family. The main technique is to fix one of the two parameters ct or k, then vary another parameter for the relation of the maximal lyapunov exponent-k or the maximal lyapunov exponent-α. Finally we give the parameter regions for chaos control and the best way to control chaos in any system of the Lorenz system family.

关 键 词：Lorenz系统族 混沌 反馈控制 

分 类 号：O415.5[理学—理论物理]