Local Lyapunov exponents computed from observed data
type: Item
instance of: scholarly article
title: Local Lyapunov exponents computed from observed data
zbMATH Open document ID: 0802.58041
DOI: 10.1007/BF01208929
published in: Journal of Nonlinear Science
publication date: 1994-06-09T00:00:00Z
review text: The Lyapunov exponents of a dynamical system quantify the growth or decay of infinitesimal perturbations to orbits of that system, the long-time growth rates refer to invariants of the dynamical system (standard exponents, named global). The paper develops the authors' earlier introduced notion [ibid. 1, No. 2, 175-199 (1991; Zbl 0797.58053)] of local Lyapunov exponents, which determine how a perturbation to a system orbit will grow in a finite time. The local exponents are shown to be derivable from observations of a scalar data set (e.g. a reconstruction of the dynamics from an experimental signal enters the scene). In several examples like Hénon map, Lorenz system, Ikeda map, it is demonstrated that the method allows one to accurately reproduce results determined when the dynamics is known beforehand.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 563615
zbMATH Keywords: chaotic dynamical system
zbMATH Keywords: Lyapunov exponents
Wikidata QID: Q56144175
author: Henry D. I. Abarbanel
author: Reggie Brown
author: Matthew B. Kennel
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01208929
OpenAlex ID: W2094890585
description: scientific article; zbMATH DE number 563615