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Synchrony for Weak Coupling in the Complexified Kuramoto Model.

Moritz Thümler1, Shesha G M Srinivas2, Malte Schröder1

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Physical Review Letters
|May 19, 2023
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Summary
This summary is machine-generated.

We analytically continued the finite-size Kuramoto model to complex variables, revealing new synchronized states. These complex locked states persist below classical phase locking, identifying subpopulations with zero mean frequency.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • The Kuramoto model describes synchronization in coupled oscillator systems.
  • Understanding collective dynamics in finite-size systems is crucial.
  • Analytical continuation extends model applicability.

Purpose of the Study:

  • To analyze the collective dynamics of the finite-size Kuramoto model extended to complex variables.
  • To investigate synchrony beyond the classical phase locking transition.
  • To identify novel synchronized states and their properties.

Main Methods:

  • Analytical continuation of the finite-size Kuramoto model from real to complex variables.
  • Analysis of attractors and stability of locked states in the complex domain.
  • Identification of subpopulations based on complex locked states.

Main Results:

  • Synchrony persists in complex locked states for coupling strengths below the classical phase locking transition (K^{(pl)}).
  • Stable complex locked states correspond to subpopulations with zero mean frequency in the real-variable model.
  • A second transition is identified where complex locked states lose linear stability but persist.

Conclusions:

  • Complexification of the Kuramoto model reveals new dynamical regimes and synchronized states.
  • Complex locked states provide insights into subpopulation structure and dynamics.
  • The study extends the understanding of synchronization phenomena in complex systems.