TY  - JOUR
A1  - Gong, Chen Chris
A1  - Pikovskij, Arkadij
T1  - Low-dimensional dynamics for higher-order harmonic, globally coupled phase-oscillator ensembles
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a low-dimensional theory in the thermodynamic limit. In this paper, we extend the formulation used by Watanabe and Strogatz to obtain a low-dimensional description of a system of arbitrary size of identical oscillators coupled all-to-all via their higher-order modes. To demonstrate an application of the formulation, we use a second harmonic globally coupled model, with a mean-field equal to the square of the Kuramoto mean-field. This model is known to exhibit asymmetrical clustering in previous numerical studies. We try to explain the phenomenon of asymmetrical clustering using the analytical theory developed here, as well as discuss certain phenomena not observed at the level of first-order harmonic coupling.
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/51407
SN  - 2470-0045
SN  - 2470-0053
VL  - 100
IS  - 6
PB  - American Physical Society
CY  - College Park
ER  -