https://doi.org/10.1140/epjp/s13360-025-06457-z
Regular Article
Synchronization of the time-delayed Kuramoto model in a regular network
1
Forschungszentrum Julich GmbH, Peter Grunberg Institut (PGI-14): Neuromorphic Compute Nodes, 52425, Julich, Germany
2
Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), 45137-66731, Zanjan, Iran
3
Department of Physics, Isfahan University of Technology, 84156-83111, Isfahan, Iran
a
s.ameli.kalkhouran@fz-juelich.de
Received:
24
March
2025
Accepted:
20
May
2025
Published online:
1
September
2025
This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective dynamics. Our analytical and numerical results reveal distinct synchronization behaviors across various time delay regimes, including fully synchronized states, helical patterns, dynamically incoherent states, and random phase-locked states. We identify the regime in which time delay inhibits synchrony, which aligns with theoretical predictions derived from stability analysis. In the region between the synchrony-possible and synchrony-forbidden zones, a coexistence of synchronized and unsynchronized dynamics is observed, referred to as chimera states. We ascertain that the type of chimera states present is moving turbulent.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
