Phase synchronization between collective rhythms of globally coupled oscillator groups: Noiseless nonidentical case
- 10 November 2010
- journal article
- research article
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 20 (4), 043110
- https://doi.org/10.1063/1.3491346
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.Keywords
This publication has 55 references indexed in Scilit:
- Existence of hysteresis in the Kuramoto model with bimodal frequency distributionsPhysical Review E, 2009
- Collective-phase description of coupled oscillators with general network structurePhysical Review E, 2009
- Long time evolution of phase oscillator systemsChaos: An Interdisciplinary Journal of Nonlinear Science, 2009
- Phase-response curves of coupled oscillatorsPhysical Review E, 2009
- Partially Integrable Dynamics of Hierarchical Populations of Coupled OscillatorsPhysical Review Letters, 2008
- Stability diagram for the forced Kuramoto modelChaos: An Interdisciplinary Journal of Nonlinear Science, 2008
- Low dimensional behavior of large systems of globally coupled oscillatorsChaos: An Interdisciplinary Journal of Nonlinear Science, 2008
- Routes to synchrony between asymmetrically interacting oscillator ensemblesPhysical Review E, 2008
- Resonance clustering in globally coupled electrochemical oscillators with external forcingPhysical Review E, 2008
- Complex networks: Structure and dynamicsPhysics Reports, 2006