Symbolic and numerical analysis for studying complex nonlinear behavior
type: Item
instance of: scholarly article
title: Symbolic and numerical analysis for studying complex nonlinear behavior
zbMATH Open document ID: 0929.65128
DOI: 10.1023/A:1019183229456
author: Safya Belghith
published in: Numerical Algorithms
publication date: 2000-01-11T00:00:00Z
review text: The technique of Carleman linearisation is used in order to derive an approximate solution of a nonlinear dynamical system (possibly depending on parameters) in terms of exponential polynomials. Using the associated variational equation approximations of the Lyapunov exponents of the system are obtained via a mixed symbolic-numerical approach. An implementation using Axiom and Fortran is described. As an example an apparently new critical value for the Lorenz system is computed. Unfortunately, the article is at many places rather sketchy, so that it is difficult to follow. Especially the interface between the symbolic and the numerical computations remains rather unclear. No comparison between the efficiency and accuracy of the new approach and traditional methods for determining Lyapunov exponents is done.
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M25
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1310133
zbMATH Keywords: Lyapunov exponents
zbMATH Keywords: Carleman linearisation
zbMATH Keywords: symbolic computation
zbMATH Keywords: nonlinear dynamical system
zbMATH Keywords: Lorenz system
reviewed by: Werner M. Seiler
MaRDI profile type: Publication
full work available at URL: a:1019183229456
OpenAlex ID: W1655748654
description: scientific article; zbMATH DE number 1310133