Multibranch entrainment and scaling in large populations of coupled oscillators

Multibranch entrainment is a peculiar mode of macroscopic synchronization in globally coupled oscillators in which a huge number of different entrained states coexist. Simulation results presented below suggest that the total number of those states, W, behaves as exp{N(g(c) - g)(3/2)} near g = g(c), where g is a control parameter, g(c) its value at the onset of multibranch entrainment, and N the system size. This implies a power law growth of an ''entropy'' of entrainment, S drop In W.