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Main Title: Hierarchical frequency clusters in adaptive networks of phase oscillators
Author(s): Berner, Rico
Fialkowski, Jan
Kasatkin, Dmitry
Nekorkin, Vladimir
Yanchuk, Serhiy
Schöll, Eckehard
Type: Article
Abstract: Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this paper, we investigate the dynamics of this system. We extend recent results on the appearance of hierarchical frequency multiclusters by investigating the effect of the time scale separation. We show that the slow adaptation in comparison with the fast phase dynamics is necessary for the emergence of the multiclusters and their stability. Additionally, we study the role of double antipodal clusters, which appear to be unstable for all considered parameter values. We show that such states can be observed for a relatively long time, i.e., they are metastable. A geometrical explanation for such an effect is based on the emergence of a heteroclinic orbit.
Subject(s): adaptive dynamical network
phase oscillators
time scale separation
hierarchical frequency multiclusters
Issue Date: 23-Oct-2019
Date Available: 23-Apr-2020
Language Code: en
DDC Class: 530 Physik
Sponsor/Funder: DFG, 411803875, Dynamik gekoppelter Systeme mit Zeitverzögerungen und deren Anwendungen
DFG, 308748074, Komplexe dynamische Netzwerke: Effekte von heterogenen, adaptiven und zeitverzögerten Kopplungen
Journal Title: Chaos: An Interdisciplinary Journal of Nonlinear Science
Publisher: American Institute of Physics (AIP)
Volume: 29
Issue: 10
Article Number: 103134
Publisher DOI: 10.1063/1.5097835
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 Chaos 29, 103134 (2019) 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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