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Main Title: Generalized splay states in phase oscillator networks
Author(s): Berner, Rico
Yanchuk, Serhiy
Maistrenko, Yuri
Schöll, Eckehard
Type: Article
Abstract: Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized m-splay states constituting a special subclass of phase-locked states with vanishing mth order parameter. Such states typically manifest incoherent dynamics, and they often create high-dimensional families of solutions (splay manifolds). For a general class of phase oscillator networks, we provide explicit linear stability conditions for splay states and exemplify our results with the well-known Kuramoto-Sakaguchi model. Importantly, our stability conditions are expressed in terms of just a few observables such as the order parameter or the trace of the Jacobian. As a result, these conditions are simple and applicable to networks of arbitrary size. We generalize our findings to phase oscillators with inertia and adaptively coupled phase oscillator models. Published under an exclusive license by AIP Publishing.
Subject(s): coordinated reset
coupled oscillators
Kuramoto model
Issue Date: 2021
Date Available: 22-Dec-2021
Language Code: en
DDC Class: 530 Physik
Sponsor/Funder: DFG, 411803875, Dynamik gekoppelter Systeme mit Zeitverzögerungen und deren Anwendungen
DFG, 440145547, Komplexe dynamische Netzwerke: Effekte von Heterogenität, Adaptivität und Topologie der Kopplungen
Journal Title: Chaos : an interdisciplinary journal of nonlinear science
Publisher: AIP Publishing
Volume: 31
Issue: 7
Article Number: 73128
Publisher DOI: 10.1063/5.0056664
EISSN: 1089-7682
ISSN: 1054-1500
Notes: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in: Berner, R., Yanchuk, S., Maistrenko, Y., & Schöll, E. (2021). Generalized splay states in phase oscillator networks. In Chaos: An Interdisciplinary Journal of Nonlinear Science (Vol. 31, Issue 7, p. 073128). AIP Publishing. and may be found at
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Theoretische Physik » FG Nichtlineare Dynamik und Kontrolle
Appears in Collections:Technische Universität Berlin » Publications

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