Synchrony for weak coupling in the complexified Kuramoto model
Abstract
We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of \textit{complex locked states} for coupling strengths below the transition to classical \textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths.
Keywords
Cite
@article{arxiv.2404.19637,
title = {Synchrony for weak coupling in the complexified Kuramoto model},
author = {Moritz Thümler and Shesha G. M. Srinivas and Malte Schröder and Marc Timme},
journal= {arXiv preprint arXiv:2404.19637},
year = {2024}
}