Coexistence of Hamiltonian-like and dissipative dynamics in chains of coupled phase oscillators with skew-symmetric coupling
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2447 | |
dc.contributor.author | Burylko, Oleksandr | |
dc.contributor.author | Mielke, Alexander | |
dc.contributor.author | Wolfrum, Matthias | |
dc.contributor.author | Yanchuk, Serhiy | |
dc.date.accessioned | 2017-12-20T08:47:29Z | |
dc.date.available | 2019-06-28T08:10:18Z | |
dc.date.issued | 2017 | |
dc.description.abstract | We consider rings of coupled phase oscillators with anisotropic coupling. When the coupling is skew-symmetric, i.e. when the anisotropy is balanced in a specific way, the system shows robustly a coexistence of Hamiltonian-like and dissipative regions in the phase space. We relate this phenomenon to the time-reversibility property of the system. The geometry of low-dimensional systems up to five oscillators is described in detail. In particular, we show that the boundary between the dissipative and Hamiltonian-like regions consists of families of heteroclinic connections. For larger chains with skew-symmetric coupling, some sufficient conditions for the coexistence are provided, and in the limit of N oscillators, we formally derive an amplitude equation for solutions in the neighborhood of the synchronous solution. It has the form of a nonlinear Schrödinger equation and describes the Hamiltonian-like region existing around the synchronous state similarly to the case of finite rings. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2136 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2722 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2447 | |
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 | Phase oscillators | eng |
dc.subject.other | reversible systems | eng |
dc.subject.other | amplitude equations | eng |
dc.title | Coexistence of Hamiltonian-like and dissipative dynamics in chains of coupled phase oscillators with skew-symmetric coupling | 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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