2019/09/30 by Chen Chris Gong, Arkady Pikovsky · 1 citation
Physics and Astronomy · #nlin.AO #nlin.CD
paper · pdf · doi:10.1103/physreve.100.062210
published as Phys. Rev. E 100, 062210 (2019) · 10 pages, 5 figures
arxiv created 2020/01/21 · arxiv updated 2020/01/22
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.