Multibranch Entrainment and Scaling in Large Populations of Coupled Oscillators.

Abstract

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 $\mathrm{exp}{N({g}_{c}\ensuremath{-}g{)}^{3/2}}$ near ${g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}g}_{c}$, 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, $S\ensuremath{\equiv}\mathrm{ln}W$.