Onset of synchronization of Kuramoto oscillators in scale-free networks

Autor(es)

Peron, Thomas ; de Resende, Bruno Messias F. ; Mata, Angelica S. ; Rodrigues, Francisco A. ; Moreno, Yamir

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW E; v. 100, n. 4, p. 8-pg., 2019-10-08.

Resumo

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent 2 < gamma <= 3, in line with what has been observed for other dynamical processes in such networks. For gamma > 3, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators. (AU)

• Processo FAPESP: 18/15589-3 - Processos Dinâmicos em Redes Ecológicas
• Beneficiário: Thomas Kaue Dal Maso Peron
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 16/25682-5 - Propagação de informação em redes complexas
• Beneficiário: Francisco Aparecido Rodrigues
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 16/23827-6 - Análise de processos epidêmicos e de sincronização em redes complexas
• Beneficiário: Thomas Kaue Dal Maso Peron
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado