Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2010-07-29
Chaos 20, 043110 (2010)
Nonlinear Sciences
Adaptation and Self-Organizing Systems
11 pages, 3 figures
Scientific paper
10.1063/1.3491346
Phase synchronization between collective oscillations exhibited by two weakly interacting groups of non-identical phase oscillators with internal and external global sinusoidal coupling of the groups is analyzed theoretically. 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. It is demonstrated that the groups can exhibit effective anti-phase 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 anti-phase external coupling between the groups.
Arai Kensuke
Kawamura Yoji
Kori Hiroshi
Kuramoto Yoshiki
Nakao Hiroya
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