A linear path toward synchronization - Anomalous scaling in a new class of exactly solvable Kuramoto models

Using a recently introduced linear reformulation of the Kuramoto model of self-synchronizing oscillator systems [1], we study a new class of analytically solvable oscillator systems defined by a particular coupling scheme. We show that these systems have a logarithmic scaling law in the vicinity of the critical point, which may be seen as anomalous with respect to the usual power-law behavior exhibited by the standard Kuramoto model.