KFU. Card publication. Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum

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APPLICATION OF THE GENERALIZED PRONY SPECTRUM FOR EXTRACTION OF INFORMATION HIDDEN IN CHAOTIC TRAJECTORIES OF TRIPLE PENDULUM

Form of presentation

Articles in international journals and collections

Year of publication

2014

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Authors, employees of KFU

Nigmatullin Ravil Rashidovich, author

Osokin Sergey Igorevich, author

Other authors

Awrejcewicz Jan , author

Kudra Grzegorz , author

Bibliographic description in the original language

Nigmatullin Raoul R., Osokin Sergey I., Awrejcewicz Jan, Kudra Grzegorz, Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum//CENTRAL EUROPEAN JOURNAL OF PHYSICS. - 2014. - Vol.12, Is.8. - P.565-577.

Annotation

In this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony's decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov's exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific ”fingerprint” characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems.

Keywords

the Prony's decomposition, chaotic behavior, triple pendulum

The name of the journal

CENTRAL EUROPEAN JOURNAL OF PHYSICS

URL

https://doi.org/10.2478/s11534-014-0485-4

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=141094&p_lang=2

Resource files

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Full metadata record

Field DC	Value	Language
dc.contributor.author	Nigmatullin Ravil Rashidovich	ru_RU
dc.contributor.author	Osokin Sergey Igorevich	ru_RU
dc.contributor.author	Awrejcewicz Jan	ru_RU
dc.contributor.author	Kudra Grzegorz	ru_RU
dc.date.accessioned	2014-01-01T00:00:00Z	ru_RU
dc.date.available	2014-01-01T00:00:00Z	ru_RU
dc.date.issued	2014	ru_RU
dc.identifier.citation	Nigmatullin Raoul R., Osokin Sergey I., Awrejcewicz Jan, Kudra Grzegorz, Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum//CENTRAL EUROPEAN JOURNAL OF PHYSICS. - 2014. - Vol.12, Is.8. - P.565-577.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=141094&p_lang=2	ru_RU
dc.description.abstract	CENTRAL EUROPEAN JOURNAL OF PHYSICS	ru_RU
dc.description.abstract	In this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony's decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov's exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific ”fingerprint” characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	the Prony's decomposition	ru_RU
dc.subject	chaotic behavior	ru_RU
dc.subject	triple pendulum	ru_RU
dc.title	Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum	ru_RU
dc.type	Articles in international journals and collections	ru_RU