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Keyword: ‘kuramoto’

## Harmony on a Donut

“Harmony” was my sloppy look at the Kuramoto model. Looking at 2 oscillators:
$\dot{\theta_1}=\omega_1+ k\sin (\theta_2-\theta_1)\\\\ \dot{\theta_2}=\omega_2+ k\sin (\theta_1-\theta_2)$

The following starts “knotted” 2:3 with $k=0$, i.e. no coupling and then increasing the coupling…another visualization of harmony.

Visualizing as motion on a circle: