Physical and emergent nonpairwise interactions in oscillator networks: from higher-order phase reduction to coupling design
Abstract
Phase reduction is a powerful technique to obtain phase models from highly dimensional oscillatory systems. Starting from pairwise interactions, a first order approximation yields Kuramoto and Winfree phase models, while nonpairwise interactions emerge at the second order. Recently, phase models have been extended to account for nonpairwise interactions, notably, the higher-order Kuramoto model. Is there an intrinsic difference between physical and emergent nonpairwise interactions? And can we make use of the former to even out the effects of the latter? In this work, we exploit a recently developed parametrization method to compute the phase reduction and answer these questions. After a comparison of the new method with the classic Kuramoto-style phase reduction, we solve the network motifs of the emergent nonpairwise interactions and compare them with the physical once. Lastly, we exploit the motifs to adopt a coupling design approach. Our framework paves the way for further exploitations of physical nonpairwise interactions for applications in synchronization engineering.
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BibTeX
@misc{muolo2026physical,
title = {{Physical and emergent nonpairwise interactions in oscillator networks: from higher-order phase reduction to coupling design}},
author = {Riccardo Muolo and Hiroya Nakao and Christian Bick},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20632},
eprint = {2609.20632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20632},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physical and emergent nonpairwise interactions in oscillator networks: from higher-order phase reduction to coupling design
AU - Riccardo Muolo
AU - Hiroya Nakao
AU - Christian Bick
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20632
UR - https://arxiv.org/abs/2609.20632
AB - Phase reduction is a powerful technique to obtain phase models from highly dimensional oscillatory systems. Starting from pairwise interactions, a first order approximation yields Kuramoto and Winfree phase models, while nonpairwise interactions emerge at the second order. Recently, phase models have been extended to account for nonpairwise interactions, notably, the higher-order Kuramoto model. Is there an intrinsic difference between physical and emergent nonpairwise interactions? And can we make use of the former to even out the effects of the latter? In this work, we exploit a recently developed parametrization method to compute the phase reduction and answer these questions. After a comparison of the new method with the classic Kuramoto-style phase reduction, we solve the network motifs of the emergent nonpairwise interactions and compare them with the physical once. Lastly, we exploit the motifs to adopt a coupling design approach. Our framework paves the way for further exploitations of physical nonpairwise interactions for applications in synchronization engineering.
ER -