Coupled Möbius maps as a tool to model Kuramoto phase synchronization

We propose Mobius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.

Metadaten
Author details:	Chen Chris Gong ORCiD, Ralf Tönjes ORCiD GND, Arkady Pikovsky ORCiD GND
DOI:	https://doi.org/10.1103/PhysRevE.102.022206
ISSN:	2470-0045
ISSN:	2470-0053
ISSN:	1063-651X
ISSN:	2470-0061
ISSN:	1550-2376
Pubmed ID:	https://pubmed.ncbi.nlm.nih.gov/32942495
Title of parent work (English):	Physical review : E, Statistical, nonlinear and soft matter physics
Publisher:	American Physical Society
Place of publishing:	College Park
Publication type:	Article
Language:	English
Date of first publication:	2020/08/12
Publication year:	2020
Release date:	2023/03/22
Volume:	102
Issue:	2
Article number:	022206
Number of pages:	12
Funding institution:	DFG/FAPESP [IRTG 1740/TRP 2015/50122-0]; [19-12-00367]; Russian Science; FoundationRussian Science Foundation (RSF) [19-12-00367] Funding Source:; Russian Science Foundation
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:	5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:	Referiert
Publishing method:	Open Access / Hybrid Open-Access
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz