Estimation of Lyapunov exponents of discrete data series

0496282 - ÚTAM 2019 RIV CZ eng A - Abstract
Fischer, Cyril - Náprstek, Jiří
Estimation of Lyapunov exponents of discrete data series.
Book of extended abstracts. 34th Conference with international participation Computational Mechanics 2018. Plzeň: University of West Bohemia, 2018 - (Adámek, V.; Jonášová, A.; Plánička, S.; Zajíček, M.). s. 21-22. ISBN 978-80-261-0819-1.
[Computational Mechanics 2018 /34./. 31.10.2018-02.11.2018, Srní]
R&D Projects: GA ČR(CZ) GC17-26353J
Institutional support: RVO:68378297
Keywords : dynamical system * non-linear system * Lyapunov exponent
OECD category: Construction engineering, Municipal and structural engineering

The dynamical systems describing general non-linear structures represent an interesting and demanding topic in various branches of engineering. In case of a complex behaviour of a structure or a non-linear mathematical model, the measured response or computed data series can exhibit wide range of response types, from stationary and periodic to diverging or chaotic behaviour. The stability in the sense of sensitivity to small perturbations, however, is the key property of each type of the system response. The concept of Lyapunov exponents (LE) is the most usable and most robust stability measure. However, practical estimation of LE for both continuous systems and discrete data is still a demanding task. Even if the topic was addressed by numerous papers in the past, it seems that the practical usage of recommended methods usually raise new questions. It is obvious because the theoretical results are mostly substantiated by an limiting relation, assumptions of which are hardly fulfilled in the practice. The case of continuous systems is often dealt in the literature. On the other hand, only rarely is mentioned the case of discrete data. The present contribution extends the previous work of the authors and aims at comparison and analysis of three approaches: two methods derived particularly for the case of discrete data series and the third one, which was originally designed for the continuous systems, but which allows a possible extension to certain discrete cases.
Permanent Link: http://hdl.handle.net/11104/0289090