title: Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case.
abstract: We theoretically investigate the collective phase synchronization between interacting groups of globally coupled noisy identical 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 individual oscillators via nonlinear Fokker-Planck equations. For sinusoidal 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.
authors.affiliation: Institute for Research on Earth Evolution, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan. ykawamura@jamstec.go.jp
authors.forename: Yoji
authors.initials: Y
authors.lastname: Kawamura
authors.forename: Hiroya
authors.initials: H
authors.lastname: Nakao
authors.forename: Kensuke
authors.initials: K
authors.lastname: Arai
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Kori
authors.forename: Yoshiki
authors.initials: Y
authors.lastname: Kuramoto