Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs
Vincent Thibeault, Benjamin Claveau, Antoine Allard, Patrick Desrosiers
Published: 2025/4/8
Abstract
Using spectral properties of the Koopman generator, we derive necessary and sufficient conditions for the existence of distinct constants of motion in the Kuramoto model with heterogeneous phase lags on any weighted, directed, signed graph. We also identify Lie symmetries that generate new constants of motion. These results reveal a broad class of network motifs that support conserved quantities and how a leader drives a group of conformist-contrarian oscillators to reach periodic states with higher average synchrony or even perfect synchrony.