关于Lyapunov指数计算方法的比较  

The Comparison for Lyapunov Exponents Calculation Methods

作　　者：张海龙[1] 闵富红[1] 王恩荣[1] 

机构地区：[1]南京师范大学电气与自动化工程学院,江苏南京210042

出　　处：《南京师范大学学报（工程技术版）》2012年第1期5-9,共5页Journal of Nanjing Normal University(Engineering and Technology Edition)

基　　金：国家自然科学基金(51075275);江苏省研究生创新工程项目(CXLX11_0889)

摘　　要：针对常用的几种Lyapunov指数数值计算方法,即定义法、正交法、wolf法和小数据量法,以典型的Lorenz系统为例,分别计算Lorenz混沌吸引子的Lyapunov指数谱或者最大Lyapunov指数,比较各种方法的计算精度、计算复杂度,并且对含噪声的混沌时间序列给出Lyapunov指数计算结果,比较各种抗干扰能力.给出了不同计算方法的性能差异、适用场合和选择依据.In this paper,the several computational methods of Lyapunov exponents are compared,i.e.,the definition method,the orthogonal method,the wolf method and the small data sets.The Lyapunov exponent power and the max-Lyapunov exponent are computed through the above methods for Lorenz system.From the results,the accuracies and the complexity of the above methods are investigated.Furthermore,the max-Lyapunov exponents are also calculated for the chaotic time series including the noise.Finally,numerical results demonstrate that the performances of different computational methods have differences,and some summaries will be presented.

关 键 词：LYAPUNOV指数 LORENZ系统 混沌系统 

分 类 号：O415[理学—理论物理]