Datum
2023-10-05Schlagwort
620 Ingenieurwissenschaften SynchronisierungDynamisches SystemGrundfrequenzParametrisierungMetadata
Zur Langanzeige
Aufsatz
Numerical detection of synchronization phenomena in quasi-periodic solutions
Zusammenfassung
In science and technology, dynamical systems can show so-called quasi-periodic solutions. These solutions are composed of two or more base frequencies. The solution in the time domain can be represented by an invariant manifold. To parametrize the invariant manifold, we choose the hyper-time parametrization. If quasi-periodic solutions branches are continued by means of a path continuation, the phenomenon of synchronization may occur. This is important, because the hyper-time parametrization is only valid, as long as the number of base frequencies remains unchanged. Therefore, it is essential to detect a parametrization to a synchronization point. Synchronization can happen in different types. We address the mechanism of suppression, where one base frequency becomes suppressed until its amplitude vanishes. This corresponds to the quasi-periodic solution ending in a Neimark–Sacker bifurcation. We present a method to derive a scalar measure from the quasi-periodic solution in the hyper-time parametrization, to detect an approach to a Neimark–Sacker bifurcation while continuing the solution branch.
Zitierform
In: Proceedings in Applied Mathematics and Mechanics (PAMM) Volume 23 / Issue 3 (2023-10-05) eissn:1617-7061Förderhinweis
Gefördert im Rahmen des Projekts DEALZitieren
@article{doi:10.17170/kobra-202311309143,
author={Seifert, Alexander and Bäuerle, Simon Andreas and Hetzler, Hartmut},
title={Numerical detection of synchronization phenomena in quasi-periodic solutions},
journal={Proceedings in Applied Mathematics and Mechanics (PAMM)},
year={2023}
}
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2023-12-15T15:38:50Z 2023-12-15T15:38:50Z 2023-10-05 doi:10.17170/kobra-202311309143 http://hdl.handle.net/123456789/15306 Gefördert im Rahmen des Projekts DEAL eng Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ 620 Numerical detection of synchronization phenomena in quasi-periodic solutions Aufsatz In science and technology, dynamical systems can show so-called quasi-periodic solutions. These solutions are composed of two or more base frequencies. The solution in the time domain can be represented by an invariant manifold. To parametrize the invariant manifold, we choose the hyper-time parametrization. If quasi-periodic solutions branches are continued by means of a path continuation, the phenomenon of synchronization may occur. This is important, because the hyper-time parametrization is only valid, as long as the number of base frequencies remains unchanged. Therefore, it is essential to detect a parametrization to a synchronization point. Synchronization can happen in different types. We address the mechanism of suppression, where one base frequency becomes suppressed until its amplitude vanishes. This corresponds to the quasi-periodic solution ending in a Neimark–Sacker bifurcation. We present a method to derive a scalar measure from the quasi-periodic solution in the hyper-time parametrization, to detect an approach to a Neimark–Sacker bifurcation while continuing the solution branch. open access Seifert, Alexander Bäuerle, Simon Andreas Hetzler, Hartmut doi:10.1002/pamm.202300235 Synchronisierung Dynamisches System Grundfrequenz Parametrisierung publishedVersion eissn:1617-7061 Issue 3 Proceedings in Applied Mathematics and Mechanics (PAMM) Volume 23 false e202300235
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