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March 4, 2024Open Access

Complexified Synchrony

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Authors

SLSeungjae LeeLBLucas BraunHBW-Gubesch Kunststoff-Engineering (Germany)FBFrieder BönischTechnische Universität Dresden

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Implication

Analysis of the Kuramoto model reveals complex locked states off the real subspace across coupled oscillators, highlighting a novel discontinuous phase transition.

Key Points

  • Complex locked states emerge off the real subspace even under arbitrarily weak complex coupling, replacing traditional phase-locked states across finite-size coupled oscillators.
  • Purely imaginary coupling prevents active synchrony across all coupling strengths, driving two-unit systems into conservative dynamics with asynchronous rotations or librations.
  • Numerical simulations for large networks indicate a novel discontinuous phase transition, supporting theoretical extensions of the Kuramoto model into the complex domain.

Cite This Study

Lee et al. (2024) studied this question.

synapsesocial.com/papers/68e75ddfb6db6435876d510chttps://doi.org/10.48550/arxiv.2403.02006
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Complexified synchrony2024 · 9 citations
  2. 2Dynamics of matrix coupled Kuramoto oscillators on modular networks: excitable behavior and global decoherence2024
  3. 3Beyond Synchronization: A Structural and Lyapunov Perspective on the Kuramoto Model2026
  4. 4Synchronization in Small, Fully Coupled Systems of Discrete-Time Kuramoto Oscillators2025
  5. 5Capturing the critical coupling of large random Kuramoto networks with graphons2025