Vortices and the entrainment transition in the 2D Kuramoto model

Details Vortices and the entrainment transition in the 2D Kuramoto model Vortices and the entrainment transition in the 2D Kuramoto model

2010-06-18

arxiv.org/abs/1006.3600v2

Phys. Rev. E 82, 036202 (2010)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 8 figures

Scientific paper

10.1103/PhysRevE.82.036202

We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling $K$ is larger than a threshold $K_E$, there is a macroscopic cluster of frequency-synchronized oscillators. We explain why the macroscopic cluster disappears at $K_E$. We view the system in terms of vortices, since cluster boundaries are delineated by the motion of these topological defects. In the entrained phase ($K>K_E$), vortices move in fixed paths around clusters, while in the unentrained phase ($K

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