一种基于多维混沌时间序列的相空间重组技术(英文)

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.

A Reconstruction Technique for Multidimensional Chaotic Time Series

Detecting the presence of chaos from deterministic time series in various fields,such as economics and biology,remains an exciting challenge.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 scalar 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 ...