Dynamical systems with multiple, long delayed feedbacks: Multiscale analysis and spatio-temporal equivalence
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2125 | |
dc.contributor.author | Yanchuk, Serhiy | |
dc.contributor.author | Giacomelli, Giovanni | |
dc.date.accessioned | 2016-12-13T10:46:42Z | |
dc.date.available | 2019-06-28T08:23:26Z | |
dc.date.issued | 2015 | |
dc.description.abstract | Dynamical systems with multiple, hierarchically long delayed feedback are introduced and studied. Focusing on the phenomenological model of a Stuart-Landau oscillator with two feedbacks, we show the multiscale properties of its dynamics and demonstrate them by means of a space-time representation. For sufficiently long delays, we derive a normal form describing the system close to the destabilization. The space and temporal variables, which are involved in the space-time representation, correspond to suitable timescales of the original system. The physical meaning of the results, together with the interpretation of the description at different scales, is presented and discussed. In particular, it is shown how this representation uncovers hidden multiscale patterns such as spirals or spatiotemporal chaos. The effect of the delays size and the features of the transition between small to large delays is also analyzed. Finally, we comment on the application of the method and on its extension to an arbitrary, but finite, number of delayed feedback terms. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2271 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3362 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Two delays | eng |
dc.subject.other | long delays | eng |
dc.subject.other | spatio-temporal representation | eng |
dc.subject.other | amplitude equations | eng |
dc.subject.other | Ginzburg-Landau equation | eng |
dc.subject.other | turbulence | eng |
dc.subject.other | spirals | eng |
dc.subject.other | defects | eng |
dc.title | Dynamical systems with multiple, long delayed feedbacks: Multiscale analysis and spatio-temporal equivalence | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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