zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A practical method for calculating largest Lyapunov exponents from small data sets. (English) Zbl 0779.58030

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.

37D45Strange attractors, chaotic dynamics