In this note, we study the emergent dynamics of the kinetic Kuramoto equation, which is a mean-field limit of the Kuramoto synchronization model. For this equation, also referred to as the Kuramoto–Sakaguchi equation Lancellotti (Transp Theory Stat Phys 34:523–535, 2005 [13]), we present two approaches for the analysis on its dynamics. First, for the system of identical oscillators, we apply a wave-front-tracking algorithm which is used for scalar conservation laws. This method gives a quantitative estimate on the approximate BV solution to the kinetic model Amadori et al. (J Differ Equ 262:978–1022, 2017, [2]). Second, we study the emergence of phase concentration phenomena by directly analyzing the dynamics of the order parameters. This can show the asymptotic behavior of the system from generic initial data Ha et al. (J Park, 2016, [8]).

Emergent dynamics for the kinetic Kuramoto equation

Amadori, D
Membro del Collaboration Group
;
2018

Abstract

In this note, we study the emergent dynamics of the kinetic Kuramoto equation, which is a mean-field limit of the Kuramoto synchronization model. For this equation, also referred to as the Kuramoto–Sakaguchi equation Lancellotti (Transp Theory Stat Phys 34:523–535, 2005 [13]), we present two approaches for the analysis on its dynamics. First, for the system of identical oscillators, we apply a wave-front-tracking algorithm which is used for scalar conservation laws. This method gives a quantitative estimate on the approximate BV solution to the kinetic model Amadori et al. (J Differ Equ 262:978–1022, 2017, [2]). Second, we study the emergence of phase concentration phenomena by directly analyzing the dynamics of the order parameters. This can show the asymptotic behavior of the system from generic initial data Ha et al. (J Park, 2016, [8]).
978-3-319-91544-9
File in questo prodotto:
File Dimensione Formato  
AP_proc_HYP(2017-02-09).pdf

non disponibili

Descrizione: Articolo principale
Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 108 kB
Formato Adobe PDF
108 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/119081
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact