arXiv subjects

Benjamin Claveau

Publications and source records attributed to Benjamin Claveau.

2 recordsLinked to original sources

arXiv2026

Operator-theoretic approach to the partial integration of randomly coupled phase oscillators

In our previous work [arXiv:2504.06248], we adopted Koopman theory to link the existence of different constants of motion to the presence of specific network motifs of Kuramoto oscillators. Yet, it remains to be shown how the partial integration can be carried out using the Koopman generator and its eigenfunctions. In this paper, we construct a random graph from network motifs that admit Koopman eigenfunctions and conserved quantities, and use it to define a partially integrable Kuramoto model. We perform the partial integration of the introduced model when there are monomial eigenfunctions and conserved cross-ratios, while providing an operator-theoretic derivation of the Watanabe-Strogatz transformation based on Magnus expansion and a recent result on closed forms of the Baker-Campbell-Hausdorff formula [arXiv:1502.06589].

math.DS↗

arXiv2025

Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs

Conserved quantities in phase-oscillator dynamics are well established for identically coupled oscillators, or groups thereof, but the explicit connectivity conditions under which more complex networks admit constants of motion remain difficult to identify. Using Koopman theory, we derive general conditions for the existence of distinct conserved quantities in the Kuramoto model with heterogeneous phase lags on any weighted, directed, and signed graph. To this end, we find Koopman eigenfunctions and continuous Lie symmetries that generate different families of constants of motion. The derived conditions reveal a broad class of network motifs that support conserved quantities and we detect these motifs in hundreds of complex empirical networks. The results thus point to connectivity patterns that can preserve phase relationships over time and motivate further investigations of Koopman spectral properties for dynamics on complex networks.

nlin.AO↗