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Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless nonidentical case
Yoji Kawamura1, Hiroya Nakao, Kensuke Arai
1Institute for Research on Earth Evolution, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan. ykawamura@jamstec.go.jp
Abstract:
We theoretically study the synchronization between collective oscillations exhibited by two weakly interacting groups of nonidentical phase oscillators with internal and external global sinusoidal couplings of the groups. Coupled amplitude equations describing the collective oscillations of the oscillator groups are obtained by using the Ott-Antonsen ansatz, and then coupled phase equations for the collective oscillations are derived by phase reduction of the amplitude equations. The collective phase coupling function, which determines the dynamics of macroscopic phase differences between the groups, is calculated analytically. We demonstrate that the groups can exhibit effective antiphase collective synchronization even if the microscopic external coupling between individual oscillator pairs belonging to different groups is in-phase, and similarly effective in-phase collective synchronization in spite of microscopic antiphase external coupling between the groups.
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