Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2010-07-26
Chaos 20, 043109 (2010)
Nonlinear Sciences
Adaptation and Self-Organizing Systems
15 pages, 7 figures
Scientific paper
10.1063/1.3491344
We theoretically investigate 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 anti-phase synchronization. We show that the macroscopic rhythms can exhibit effective anti-phase 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.
Arai Kensuke
Kawamura Yoji
Kori Hiroshi
Kuramoto Yoshiki
Nakao Hiroya
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