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This is a Quantitative Study study.

October 13, 2025Open Access

Quantitative relaxation dynamics from generic initial configurations in the inertial Kuramoto model

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The framework identifies conditions for achieving a phase-locked state from various initial configurations.
Three dynamic stages are observed: the initial layer, condensation, and relaxation phases lead toward phase-locking.
A positive initial order parameter and controlled coupling strength are essential for stability during the dynamics.
The study employs advanced mathematical tools like a nonlinear Grönwall inequality and the Łojasiewicz gradient theorem for proof.

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This analysis explores relaxation dynamics and phase-locking conditions in the inertial Kuramoto model, suggesting specific criteria for stability.

Cho et al. (2025) studied this question.

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This analysis explores relaxation dynamics and phase-locking conditions in the inertial Kuramoto model, suggesting specific criteria for stability.