Synchrony for Weak Coupling in the Complexified Kuramoto Model

Research output: Contribution to journalResearch articleContributedpeer-review



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 complex locked states for coupling strengths K below the transition K(pl) to classical phase locking. Stable complex locked states indicate a locked subpopulation of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that subpopulation. We uncover a second transition at K′<K(pl) below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths.


Original languageEnglish
Article number187201
JournalPhysical review letters
Issue number18
Publication statusPublished - 3 May 2023

External IDs

Scopus 85158879829
Mendeley b4a6e0fc-fb0f-3908-a53b-5d5e893adfdf
WOS 000988178500010
ORCID /0000-0002-5956-3137/work/142242539