Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions

Fuente: arXiv
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Main Authors: Costa, Guilherme S., Novaes, Marcel, Fariello, Ricardo, de Aguiar, Marcus A. M.
Format: Preprint
Published: 2025
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author Costa, Guilherme S.
Novaes, Marcel
Fariello, Ricardo
de Aguiar, Marcus A. M.
author_facet Costa, Guilherme S.
Novaes, Marcel
Fariello, Ricardo
de Aguiar, Marcus A. M.
contents We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics of the order parameter, allowing for a full dimensional reduction of this system. We discuss how such reduction can be implemented in two different ways and how they are related. When restricted to the equator, the dynamics is similar to that of the usual Kuramoto model, up to an interesting renormalization of the coupling constants. Outside this plane, the motion reduces to a two-parameter set of periodic orbits. We also locate the bifurcation curves of the system as functions of different parameters.
format Preprint
id arxiv_https___arxiv_org_abs_2505_17255
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions
Costa, Guilherme S.
Novaes, Marcel
Fariello, Ricardo
de Aguiar, Marcus A. M.
Adaptation and Self-Organizing Systems
Physics and Society
We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics of the order parameter, allowing for a full dimensional reduction of this system. We discuss how such reduction can be implemented in two different ways and how they are related. When restricted to the equator, the dynamics is similar to that of the usual Kuramoto model, up to an interesting renormalization of the coupling constants. Outside this plane, the motion reduces to a two-parameter set of periodic orbits. We also locate the bifurcation curves of the system as functions of different parameters.
title Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions
topic Adaptation and Self-Organizing Systems
Physics and Society
url https://arxiv.org/abs/2505.17255