  Using a recently introduced linear reformulation of the Kuramoto model of
self-synchronizing oscillator systems (arXiv:0704.1166), we study a new class
of analytically solvable oscillator systems defined by a particular coupling
scheme. We show that these systems have a logarithimic 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.
