A practical method for calculating largest Lyapunov exponents from small data sets
type: Item
instance of: scholarly article
title: A practical method for calculating largest Lyapunov exponents from small data sets
zbMATH Open document ID: 0779.58030
DOI: 10.1016/0167-2789(93)90009-P
author: Michael T. Rosenstein
author: James J. Collins
author: Carlo J. De Luca
published in: Physica D
publication date: 1993-08-18T00:00:00Z
review text: This paper addresses the problem of calculating the largest Lyapunov exponents of a dynamical system from small sets of experimental data. The authors have devised an algorithm which they claim to be fast, easily implemented, and robust to changes in embedding dimension, size of the data set, reconstruction delay, and noise level. The current most popular algorithm for quantifying chaotic behavior is the Grassberger-Procaccia method, but this algorithm is sensitive to small variations in parameters, and generally requires long, noise-free time series. The authors of this paper note that calculation of the largest Lyapunov exponents is the most direct method for quantifying chaotic behavior manifested in time series produced by dynamical systems. However, the largest Lyapunov exponent has proven difficult to estimate for small data sets, and existing algorithms to compute it are computationally intensive and difficult to implement. The new algorithm which the authors present is direct and efficient, and is capable of estimating the correlation dimension as well as the largest Lyapunov exponent.
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 269574
zbMATH Keywords: largest Lyapunov exponent
zbMATH Keywords: Grassberger-Procaccia algorithm
zbMATH Keywords: time series
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
cites work: Using higher-order correlations to define an embedding window
cites work: Extracting qualitative dynamics from experimental data
cites work: Nonlinear prediction of chaotic time series
cites work: Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
cites work: Ergodic theory of chaos and strange attractors
cites work: Chaotic time series analyses of epileptic seizures
cites work: Independent coordinates for strange attractors from mutual information
cites work: A two-dimensional mapping with a strange attractor
cites work: Deterministic Nonperiodic Flow
cites work: Oscillation and Chaos in Physiological Control Systems
cites work: Q5646734
cites work: The statistical properties of dimension calculations using small data sets
cites work: An equation for hyperchaos
cites work: An equation for continuous chaos
cites work: A numerical approach to ergodic problem of dissipative dynamical systems.
cites work: Calculation of Lyapunov exponents avoiding spurious elements
cites work: Q3658782
cites work: Determining Lyapunov exponents from a time series
description: scientific article