How to extract Lyapunov exponents from short and noisy time series

Author

Banbrook, M. ; Ushaw, G. ; McLaughlin, S.

Author_Institution

Dept. of Electr. Eng., Edinburgh Univ., UK

Volume

45

Issue

5

fYear

1997

fDate

5/1/1997 12:00:00 AM

Firstpage

1378

Lastpage

1382

Abstract

In this correspondence, we discuss an algorithm for the extraction of Lyapunov spectra from short and noisy time series. Initially, we briefly describe an existing algorithm and include a method for improving the robustness to noise of this algorithm. The problem of short time series is then addressed, and a novel concatenation technique is presented and combined with the extraction algorithm previously utilized. Results of applying this extended algorithm to chaotic time series are presented, and the effects of noise and data length are discussed

Keywords

Lyapunov methods; chaos; noise; nonlinear dynamical systems; spectral analysis; time series; Lyapunov exponents; Lyapunov spectra; chaotic time series; composite attractor; concatenation technique; extraction algorithm; noisy time series; robustness to noise; short time series; Adaptive filters; Adaptive signal processing; Algorithm design and analysis; Circuits; Eigenvalues and eigenfunctions; Filtering algorithms; Least squares approximation; Notice of Violation; Signal processing algorithms; Speech processing;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.575715

Filename

575715