一种基于多维混沌时间序列的相空间重组技术(英文)  

A Reconstruction Technique for Multidimensional Chaotic Time Series

作　　者：赵梅春[1,2] 

机构地区：[1]广东金融学院应用数学系,广东广州510521 [2]中山大学数学与计算科学学院,广东广州510275

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2009年第4期379-386,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：Project Supported by the Natural Science Foundation of Guangdong Province(50033047)

摘　　要：对给定的标量时间序列,利用Takens嵌入定理展开时间序列到高维并重构未知系统的吸引子,是从时间序列寻找决定性混沌证据的常用方法.在传统的一维时间序列重构技术基础上,提出一种更有效的多维时间序列相空间重构技术.对一些已知混沌系统如洛伦兹系统、陈系统、罗莎系统、罗宾系统和罗莎超混沌系统进行了重构.结果表明,与传统的重构技术相比,多维重构技术计算出的最大李雅普洛夫指数更精确,对于非混沌系统和附加噪音的混沌系统,多维重构技术也表现出一定的优势.Detecting the presence of chaos from deterministic time series in various fields,such as economics and biology, remains an exciting ehallenge. A common practice in chaotic time series analysis is to reconstruct an attractor in phase space by utilizing the delay embedding technique, that is, given a sealar time series, the attractor of an （unknown） underlying dynamical system can be reconstructed by unfolding the time series to a higher dimensional time series according to Taken＇s theorem of embedding. In contrast to conventional reconstruction technique, where the time series of only a single variable of the unknown system is available for the reconstruction and characterization of an attractor, in this paper we present a new technique to perform meaningful reconstruction in the phase space using multidimensional data. To demonstrate the efficiency of our technique, we reeonstructed chaotic attractors from multidimensional time series of several existing chaotic systems, such as the Lorenz system, Chen system, Rossler system, Robinovieh-fabrikant system and Rossler-hyperchaos system. The results show that the large Lyapunov exponent is more accurate than that estimated from using conventional embedding methods. Even in the cases of non-chaotic and additive noise chaotic systems, our reconstruction technique can perform well.

关 键 词：重构 李雅普洛夫指数 多维时间序列 Takens嵌入定理 

分 类 号：O415.5[理学—理论物理]