Journal ArticleDOI
Measurement of the Lyapunov spectrum from a chaotic time series.
Masaki Sano,Yasuji Sawada +1 more
TLDR
A new method is proposed to determine the spectrum of several Lyapunov exponents (including positive, zero, and even negative ones) from the observed time series of a single variable.Abstract:
The exponential divergence or convergence of nearby trajectories (Lyapunov exponents) is conceptually the most basic indicator of deterministic chaos. We propose a new method to determine the spectrum of several Lyapunov exponents (including positive, zero, and even negative ones) from the observed time series of a single variable. We have applied the method to various known model systems and also to the Rayleigh-B\'enard experiment, and have elucidated the dependence of the Lyapunov exponents on the Rayleigh number.read more
Citations
More filters
Journal ArticleDOI
Testing for nonlinearity in time series: the method of surrogate data
TL;DR: In this article, a statistical approach for identifying nonlinearity in time series is described, which first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate sets.
Testing for nonlinearity in time series: The method of surrogate data
TL;DR: A statistical approach for identifying nonlinearity in time series which is demonstrated for numerical data generated by known chaotic systems, and applied to a number of experimental time series, which arise in the measurement of superfluids, brain waves, and sunspots.
Journal ArticleDOI
A practical method for calculating largest Lyapunov exponents from small data sets
TL;DR: A new method for calculating the largest Lyapunov exponent from an experimental time series is presented that is fast, easy to implement, and robust to changes in the following quantities: embedding dimension, size of data set, reconstruction delay, and noise level.
Journal ArticleDOI
The analysis of observed chaotic data in physical systems
TL;DR: Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field as mentioned in this paper, and many tools have been developed for the analysis of such data.
Journal ArticleDOI
Practical implementation of nonlinear time series methods: The TISEAN package.
TL;DR: In this paper, the authors describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos and present a variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation.