分数阶Chen混沌系统的复合结构分析  

The Compound Structure of Fractional Order Chaotic Chen's Attractor

作　　者：李新杰[1] 刘杰[1,2] 董鹏真[1] 邢丽芬[1] 

机构地区：[1]武汉科技学院非线性科学研究中心,湖北武汉430073 [2]武汉科技学院理学院,湖北武汉430073

出　　处：《武汉科技学院学报》2009年第2期30-34,共5页Journal of Wuhan Institute of Science and Technology

基　　金：武汉科技学院院基金No:20073201;武汉科技学院国家级项目孵化预研基金;湖北省自然科学基金面上项目No:2007ABA348资助的课题~~

摘　　要：首先依照分数阶非线性系统出现混沌的必要条件,分析了分数阶Chen系统出现混沌现象的阶次范围;之后,基于分数阶微积分的预估-校正算法,对该类系统进行了动力学行为的数值仿真研究。进一步,通过引入了一个常数控制器,数值地讨论了分数阶Chen系统混沌吸引子的特殊复合结构,研究发现:导致该复合结构出现的常量控制器幅值大小与受控系统的倍周期分岔点密切相关,具体表现为:系统阶次参数越高,导致受控分数阶Chen系统的倍周期分岔点出现的常数控制器的幅值绝对值越大,这一结果对于了解分数阶Chen混沌系统的吸引子复合结构无疑具有一定参考意义。In this paper, the range of order for the Chen＇ s system behaving chaotic is investigated based on a necessary condition for the existence of double scroll attractor in fractional order dynamical systems firstly. Then,dynamics analysis of the fractional Chen＇ s system is carried out numerically via bifurcation analysis based on the modified predictor-corrector algorithm for fractional ODEs. Forethermore,we investigated the compound constructure of fractinal order Chen＇ s attractor. It is found that,the constant controlling＇ s strength value,which leads to the compound constructure, is closely related to the period-doubling bifurcation point of controlled system. Generally speaking,the higher the order parameter is,the larger absolute value of the constant controllor will be,at which point it will occurs doubling period bifuration in the controlled Chen＇ s system. Our research has some hints for understanding the compound structure of the fractional order dynamical attractor similar with the Chen＇ s attrator.

关 键 词：分数阶Chen系统 预估-校正算法 复合结构 常量控制器 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]