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Using a recently introduced linear reformulation of the Kuramoto model ofself-synchronizing oscillator systems (arXiv:0704.1166), we study a new classof analytically solvable oscillator systems defined by a particular couplingscheme. We show that these systems have a logarithimic scaling law in thevicinity of the critical point, which may be seen as anomalous with respect tothe usual power-law behavior exhibited by the standard Kuramoto model.

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