L1D2（最大李雅普诺夫指数估计与时间序列的关联维计算程序

hillside

      以下内容摘自生理学软件库网站（http://physionet.org/physiotools/software-index.shtml），其中的交叉谱、能量谱、非线性时间序列统计分析对于气象研究可能有很好的借鉴、对比作用。
     为使网友们能够更清楚地了解它的功用，现对部分程序拆零介绍。
        A practical method for calculating largest Lyapunov exponents from small data setsM.T. Rosenstein, J.J. Collins, and C.J. De Luca.A practical method for calculating largest Lyapunov exponents from small data sets

This article originally appeared in Physica D 65:117-134, 1993. Please cite this publication when referencing this material. Software that implements the algorithm described by this article may be found here.

Abstract

Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest Lyapunov exponent. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. We present a new method for calculating the largest Lyapunov exponent from an experimental time series. The method follows directly from the definition of the largest Lyapunov exponent and is accurate because it takes advantage of all the available data. We show that the algorithm is fast, easy to implement, and robust to changes in the following quantities: embedding dimension, size of data set, reconstruction delay, and noise level. Furthermore, one may use the algorithm to calculate simultaneously the correlation dimension. Thus, one sequence of computations will yield an estimate of both the level of chaos and the system complexity.

The full article may be downloaded in PDF (783KB) or gzip-compressed PostScript (361KB) formats.

See also

Visualizing the effects of filtering chaotic signals

Reconstruction expansion as a geometry-based framework for choosing proper delay times

emina

高级{:5_235:}