Phase synchronization between collective rhythms of globally coupled oscillator groups: Noisy DEentical case

摘要

We theoretically investigate the collective phase synchronization between interacting groups of globally coupled noisy DEentical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective phase equations describing the macroscopic rhythms of the groups from microscopic Langevin phase equations of the indivDEual oscillators via nonlinear Fokker-Planck equations. For sinusoDEal microscopic coupling, we determine the type of the collective phase coupling function, i.e., whether the groups exhibit in-phase or antiphase synchronization. We show that the macroscopic rhythms can exhibit effective antiphase synchronization even if the microscopic phase coupling between the groups is in-phase, and vice versa. Moreover, near the onset of collective oscillations, we analytically obtain the collective phase coupling function using center-manifold and phase reductions of the nonlinear Fokker-Planck equations.