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 expN(gc-g)3/2 near g0ex0ex=0ex0exgc, where g is a control parameter, gc 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≡lnW.