Phase Locking in Oscillator Networks with Uncertain and State-Dependent Couplings
Abstract
Phase locking in oscillator networks depends critically on the interaction strengths between coupled units. In many applications, however, these couplings are uncertain, state dependent, or time varying. We derive rigorous conditions for phase locking in Kuramoto-type networks when each coupling strength is known only within prescribed bounds. Building on a convex formulation of the nonlinear fixed-point equations, we obtain edge-wise error bounds for arbitrary feasible approximations that hold uniformly over all admissible couplings. These bounds yield sufficient conditions for the existence of phase-locked states with prescribed phase-difference limits. We illustrate the framework for AC power grids with uncertain voltage magnitudes and adaptive oscillator networks with state-dependent couplings. For the latter, the bounds can be further tightened by exploiting the state dependence of the couplings.
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BibTeX
@misc{bacic2026phase,
title = {{Phase Locking in Oscillator Networks with Uncertain and State-Dependent Couplings}},
author = {Iva Bačić and Philipp C. Böttcher and Marc Hunkemöller and Carsten Hartmann and David Gross and Andrea Benigni and Dirk Witthaut},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06466},
eprint = {2611.06466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06466},
}
RIS
TY - UNPB
TI - Phase Locking in Oscillator Networks with Uncertain and State-Dependent Couplings
AU - Iva Bačić
AU - Philipp C. Böttcher
AU - Marc Hunkemöller
AU - Carsten Hartmann
AU - David Gross
AU - Andrea Benigni
AU - Dirk Witthaut
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06466
UR - https://arxiv.org/abs/2611.06466
AB - Phase locking in oscillator networks depends critically on the interaction strengths between coupled units. In many applications, however, these couplings are uncertain, state dependent, or time varying. We derive rigorous conditions for phase locking in Kuramoto-type networks when each coupling strength is known only within prescribed bounds. Building on a convex formulation of the nonlinear fixed-point equations, we obtain edge-wise error bounds for arbitrary feasible approximations that hold uniformly over all admissible couplings. These bounds yield sufficient conditions for the existence of phase-locked states with prescribed phase-difference limits. We illustrate the framework for AC power grids with uncertain voltage magnitudes and adaptive oscillator networks with state-dependent couplings. For the latter, the bounds can be further tightened by exploiting the state dependence of the couplings.
ER -