Computation of Lyapunov spectra: Effect of interactive noise and application to a chemical oscillator
type: Item
instance of: scholarly article
title: Computation of Lyapunov spectra: Effect of interactive noise and application to a chemical oscillator
zbMATH Open document ID: 0774.58028
DOI: 10.1016/0167-2789(93)90150-Y
author: Th.-M. Kruel
author: F. W. Schneider
author: Markus Eiswirth
published in: Physica D
publication date: 1993-06-29T00:00:00Z
review text: This paper essentially presents an algorithm for the computation of the Lyapunov exponents of a flow over a manifold. The authors have choosen the Jacobian method, this means that one has to exhibit a basis of the tangent space at points distributed along a trajectory and to compute the matrix of the linear tangent map. This matrix is obtained by the least squares approximation and the authors discuss the accuracy of the method with respect to some parameters (time step, geometrical position of the increments in the computation of the tangent space,...). The results are presented for various attractors (Rössler, Lorentz, Brusselator,...) and exhibit chaotic or hyperchaotic behavior at different regimes.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37N99
zbMATH DE Number: 221904
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: attractors
reviewed by: Jean Lacroix
MaRDI profile type: Publication
cites work: Q3998284
cites work: Q3736576
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cites work: An equation for hyperchaos
cites work: Q3715933
cites work: Determining Lyapunov exponents from a time series
cites work: Ergodic theory of chaos and strange attractors
cites work: An equation for continuous chaos
cites work: Q4089696
cites work: Q3713483
cites work: Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
cites work: Topological dimension and local coordinates from time series data
cites work: Lyapunov exponents from observed time series
cites work: Q4692890
cites work: Numerical simulations of stochastic differential equations
cites work: IDENTIFICATION OF TRUE AND SPURIOUS LYAPUNOV EXPONENTS FROM TIME SERIES
full work available at URL: 0167-2789(93)90150-y
OpenAlex ID: W2014070375
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description: scientific article; zbMATH DE number 221904