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 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.

  • Received 2 June 2022
  • Revised 10 March 2023
  • Accepted 4 April 2023


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Nonlinear Dynamics

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