Estimating the Largest Lyapunov Exponent Based on Conditional Number

The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed and developed for its calculation. The present work proposes...

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Bibliographic Details
Published inarXiv.org
Main Authors Silva, Pedro H O, Vinícius da Silva Borges, Guedes, Priscila F S, Silva, Igor C, Nepomuceno, Erivelton G
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.11.2017
Subjects
Chaos theory
Dynamic response
Dynamic stability
Liapunov exponents
Mathematical analysis
Rounding
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Summary:The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed and developed for its calculation. The present work proposes a method for the calculation of the largest Lyapunov exponent, based on conditional number of the function, which describes the loss of bits in the simulation based on relative rounding error. Four discrete maps are used to show the effectiveness of the proposed method.
ISSN:2331-8422