Global weak solutions exist for the continuum Kuramoto model with fractional Laplacian-type non-integrable kernels and relax exponentially to the phase average under suitable conditions.
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The singular continuum Kuramoto model exhibits complete phase synchronization in finite time for identical natural frequencies and practical synchronization for non-identical frequencies, with a rigorous graph limit from finite singular Kuramoto systems.
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Relaxation dynamics of the continuum Kuramoto model with non-integrable kernels
Global weak solutions exist for the continuum Kuramoto model with fractional Laplacian-type non-integrable kernels and relax exponentially to the phase average under suitable conditions.
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Emergent behaviors of the singular continuum Kuramoto model and its graph limit
The singular continuum Kuramoto model exhibits complete phase synchronization in finite time for identical natural frequencies and practical synchronization for non-identical frequencies, with a rigorous graph limit from finite singular Kuramoto systems.