alpha-KURAMOTO PARTITIONS FROM THE FRUSTRATED KURAMOTO MODEL GENERALISE EQUITABLE PARTITIONS

The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An α-Kuramoto partition is a graph partition induced by the Kuramoto model, when the oscillators include a phase frustration parameter. We prove that every equitable partition is an α-Kuramoto partition, but that the converse does necessarily not hold. We give an exact characterization of α-Kuramoto bipartitions.