@article{8462cde73d30435c9f87cd2771682537,
title = "Multiple Self-Locking in the Kuramoto-Sakaguchi System with Delay",
abstract = "We study the Kuramoto-Sakaguchi system of phase oscillators with a delayed mean-field coupling. By applying the theory of large delay to the corresponding Ott-Antonsen equation, we explain fully analytically the mechanisms for the appearance of multiple coexisting partially locked states. Closely above the onset of synchronization, these states emerge in the Eckhaus scenario: With increasing coupling, more and more partially locked states appear unstable from the incoherent state and gain stability for larger coupling at a modulational stability boundary. The partially locked states with strongly detuned frequencies are shown to emerge subcritical and gain stability only after a fold and a series of Hopf bifurcations. We also discuss the role of the Sakaguchi phase lag parameter. For small delays, it determines, together with the delay time, the attraction or repulsion to the central frequency, which leads to supercritical or subcritical behavior, respectively. For large delay, the Sakaguchi parameter does not influence the global dynamical scenario.",
keywords = "synchronization, large delay, modulational instability, COUPLED OSCILLATORS, MODEL, BIFURCATIONS, SPECTRUM",
author = "M. Wolfrum and S. Yanchuk and O. D'Huys",
note = "Funding Information: \ast Received by the editors November 11, 2021; accepted for publication (in revised form) by L. DeVille April 1, 2022; published electronically July 5, 2022. https://doi.org/10.1137/21M1458971 Funding: The work of the first author was supported by the German Science Foundation (Deutsche Forschungs-gemenschaft, DFG) within Collaborative Research Center SFB 910 Project 163436311. The work of the second author was supported by the German Science Foundation (Deutsche Forschungsgemenschaft, DFG) within Collaborative Research Center SFB 910 Project 411803875. The work of the third author was supported by the European Union's Horizon 2020 research and innovation program under Marie Sklodowska-Curie grant 713694. \dagger Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany (
[email protected]). \ddagger Technische Universit\a{"}t Berlin, 10623 Berlin, Germany (
[email protected]). \S Department of Data Science and Knowledge Engineering, Maastricht University, 6211 LK Maastricht, the Netherlands (
[email protected]). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics",
year = "2022",
doi = "10.1137/21M1458971",
language = "English",
volume = "21",
pages = "1709--1725",
journal = "Siam Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society of Industrial and Applied Mathematics",
number = "3",
}