Physical and emergent nonpairwise interactions in oscillator networks: from higher-order phase reduction to coupling design
Year: 2026
Type: preprint
Abstract: Phase reduction is a powerful technique to obtain phase models from high 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 derive 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1414789542, Synchronization dynamics and dimensionality reduction in coupled dynamical systems on hypergraphs, Machine Learning for Prediction and Control of Complex Dynamics Based on Integration of Mathematical and Data-Driven Methods, G8080901651, G8208761268, Systematic extraction of key dynamical structures, prediction, and control of nonlinear systems
OpenAlex ID: W7213581761