Conservative dynamics in phase oscillator networks
Chaotic Dynamics
2026-03-27 v1 Adaptation and Self-Organizing Systems
Abstract
The interaction between phase oscillators is conservative if the phase volume is conserved throughout the dynamics. We derive a general condition, based on the notion of a pair-Hamiltonian, for the pairwise couplings to be conservative. The conservative networks with Winfree-type and Kuramoto-Daido-type couplings are also discussed. It is demonstrated that although, in contradistinction to genuine Hamiltonian dynamics, there is no exact pairwise symmetry of the Lyapunov exponents, the Lyapunov spectrum for a large network is nearly symmetric. The concept is also generalized to triplet and quadruplet couplings.
Cite
@article{arxiv.2603.25431,
title = {Conservative dynamics in phase oscillator networks},
author = {Arkady Pikovsky},
journal= {arXiv preprint arXiv:2603.25431},
year = {2026}
}