Work

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

Year: 2025

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

Authors: Costa, Guilherme S., Novaes, Marcel, Fariello, Ricardo, de Aguiar, Marcus A. M.

Institutions: ICTP South American Institute for Fundamental Research, Universidade Estadual de Campinas (UNICAMP), Universidade Federal de Uberlândia, Universidade Estadual de Montes Claros, Universidade Estadual Paulista (Unesp)

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico

Awards: G1532143087, Multi-user Equipmente approved in grant 2013/08293-7, KAHUNA upgrade - HPE Apollo Gen10 supercomputer, G187716650, G2065082359, G2567384294, G295657101, G4121496537, G4910255078, Generalizations and Applications of the Kuramoto model, ICTP South American Institute for Fundamental Research: a regional center for Theoretical Physics, G6438247056, G7012276532, G7947704863, CCES - Center for Computational Engineering and Sciences

OpenAlex ID: W6979373402

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