Universität zu Köln

Schroeder, Malte, Timme, Marc ORCID: 0000-0002-5956-3137 and Witthaut, Dirk ORCID: 0000-0002-3623-5341 (2017). A universal order parameter for synchrony in networks of limit cycle oscillators. Chaos, 27 (7). MELVILLE: AMER INST PHYSICS. ISSN 1089-7682

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Abstract

We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the introduced order parameters capture all transitions from incoherence over phase locking to full synchrony for arbitrary, finite networks. We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network topology and its influence on the phase coherence of the oscillators. We rigorously prove that this order parameter is strictly monotonously increasing with the coupling strength in the phase locked state, directly reflecting the dynamic stability of the network. Furthermore, it indicates the onset of full phase locking by a diverging slope at the critical coupling strength. The order parameter may find applications across systems where different types of synchrony are possible, including biological networks and power grids. Published by AIP Publishing.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schroeder, Malte UNSPECIFIED UNSPECIFIED UNSPECIFIED Timme, Marc UNSPECIFIED orcid.org/0000-0002-5956-3137 UNSPECIFIED Witthaut, Dirk UNSPECIFIED orcid.org/0000-0002-3623-5341 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-225677
DOI:	10.1063/1.4995963
Journal or Publication Title:	Chaos
Volume:	27
Number:	7
Date:	2017
Publisher:	AMER INST PHYSICS
Place of Publication:	MELVILLE
ISSN:	1089-7682
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language COMPLEX NETWORKS; COUPLED OSCILLATORS; DIRECTED NETWORKS; PHASE OSCILLATORS; SUPPLY NETWORKS; TRANSITIONS; DYNAMICS; KURAMOTO; MODEL Multiple languages Mathematics, Applied; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/22567