Synchrony for Weak Coupling in the Complexified Kuramoto Model

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 co...

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Bibliographic Details
Published in:Physical review letters 2023-05, Vol.130 (18), p.187201-187201, Article 187201
Main Authors: Thümler, Moritz, Srinivas, Shesha G M, Schröder, Malte, Timme, Marc
Format: Article
Language:English
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Summary: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^{'}
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.130.187201