Generic scaling at the onset of macroscopic mutual entrainment in limit-cycle oscillators with uniform all-to-all coupling

The order function theory developed recently to deal with phase models of limit-cycle oscillators with uniform all-to-all coupling reveals that the critical exponent of an order parameter at the onset of macroscopic mutual entrainment is one for generic coupling functions, differing from the mean-field value 1/2 taken by the well-studied model with sinusoidal coupling. This result is supported by numerical simulation.