Exact solutions of the Kuramoto model with asymmetric higher order interactions of arbitrary order

Autor(es)

Costa, Guilherme S. ; Novaes, Marcel ; de Aguiar, Marcus A. M.

• Tipo de documento: Artigo Científico
• Fonte: CHAOS SOLITONS & FRACTALS; v. 195, p. 6-pg., 2025-03-13.

Resumo

Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible functional forms, depending on how exactly the bodies are coupled. Which of these forms is better suited to describe the dynamics of the oscillators depends on the specific system under consideration. Here we show that, for a particular class of interactions, reduced equations for the Kuramoto order parameter can be derived for arbitrarily many bodies. Moreover, the contribution of a given term to the reduced equation does not depend on its order, but on a certain effective order, that we define. We give explicit examples where bi and tri-stability is found and discuss a few exotic cases where synchronization happens via a third order phase transition. (AU)

• Processo FAPESP: 21/14335-0 - ICTP Instituto Sul-Americano para Física Fundamental: um centro regional para Física Teórica
• Beneficiário: Nathan Jacob Berkovits
• Modalidade de apoio: Auxílio à Pesquisa - Projetos Especiais
• Processo FAPESP: 23/15644-2 - Generalizações e Aplicações do modelo de Kuramoto
• Beneficiário: Marcus Aloizio Martinez de Aguiar
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil
• Processo FAPESP: 23/03917-4 - Sincronização de osciladores de Kuramoto frustrados em redes modulares
• Beneficiário: Guilherme Henrique da Silva Costa
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado