Multistability of twisted states in non-locally coupled Kuramoto-type models
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1685 | |
dc.contributor.author | Girnyk, Taras | |
dc.contributor.author | Hasler, Martin | |
dc.contributor.author | Maistrenko, Yuriy | |
dc.date.accessioned | 2016-03-24T17:39:06Z | |
dc.date.available | 2019-06-28T08:09:01Z | |
dc.date.issued | 2012 | |
dc.description.abstract | A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without limitation of the generality the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type and therefore all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2 pi q/N are equilibrium points, where q is an integer. Their stability in the limit N -> inf. is discussed along the line of1. In addition we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2 pi q/N in one sector of the ring, -2 pi q/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N -> inf. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N -> 1. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2703 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2622 | |
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 | Chaos | eng |
dc.subject.other | Nonlinear dynamical systems | eng |
dc.subject.other | Numerical analysis | eng |
dc.subject.other | Oscillators | eng |
dc.title | Multistability of twisted states in non-locally coupled Kuramoto-type models | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.subject | Physik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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