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Title: Strategies for computation of Lyapunov exponents estimates from discrete data (English)
Author: Fischer, Cyril
Author: Náprstek, Jiří
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Hejnice, June 24-29, 2018
Issue: 2018
Pages: 55-62
Category: math
Summary: The Lyapunov exponents (LE) provide a simple numerical measure of the sensitive dependence of the dynamical system on initial conditions. The positive LE in dissipative systems is often regarded as an indicator of the occurrence of deterministic chaos. However, the values of LE can also help to assess stability of particular solution branches of dynamical systems. The contribution brings a short review of two methods for estimation of the largest LE from discrete data series. Two methods are analysed and their freely available Matlab implementations are tested using two sets of discrete data: the sampled series of the Lorenz system and the experimental record of the movement of a~heavy ball in a spherical cavity. It appears that the most important factor in LE estimation from discrete data series is quality of the available record. (English)
Keyword: dynamical system
Keyword: Lyapunov exponents
Keyword: stability
Keyword: data analysis
MSC: 34C25
MSC: 34D30
MSC: 37M10
MSC: 37M25
DOI: 10.21136/panm.2018.06
Date available: 2019-04-29T13:16:54Z
Last updated: 2021-05-05
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