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On the number of stable solutions in the Kuramoto model

  • Dades identificatives

    Identificador: imarina:9330276
    Autors:
    Arenas, AlexGarijo, AntonioGomez, SergioVilladelprat, Jordi
    Resum:
    We consider a system of n coupled oscillators described by the Kuramoto model with the dynamics given by θ˙=ω+Kf(θ). In this system, an equilibrium solution θ∗ is considered stable when ω+Kf(θ∗)=0, and the Jacobian matrix Df(θ∗) has a simple eigenvalue of zero, indicating the presence of a direction in which the oscillators can adjust their phases. Additionally, the remaining eigenvalues of Df(θ∗) are negative, indicating stability in orthogonal directions. A crucial constraint imposed on the equilibrium solution is that |Γ(θ∗)|≤π, where |Γ(θ∗)| represents the length of the shortest arc on the unit circle that contains the equilibrium solution θ∗. We provide a proof that there exists a unique solution satisfying the aforementioned stability criteria. This analysis enhances our understanding of the stability and uniqueness of these solutions, offering valuable insights into the dynamics of coupled oscillators in this system.
  • Altres:

    Autor segons l'article: Arenas, Alex; Garijo, Antonio; Gomez, Sergio; Villadelprat, Jordi
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Arenas Moreno, Alejandro / Garijo Real, Antonio / Gómez Jiménez, Sergio / Villadelprat Yagüe, Jordi
    Codi de projecte: PID2020-118281GB-C33
    Resum: We consider a system of n coupled oscillators described by the Kuramoto model with the dynamics given by θ˙=ω+Kf(θ). In this system, an equilibrium solution θ∗ is considered stable when ω+Kf(θ∗)=0, and the Jacobian matrix Df(θ∗) has a simple eigenvalue of zero, indicating the presence of a direction in which the oscillators can adjust their phases. Additionally, the remaining eigenvalues of Df(θ∗) are negative, indicating stability in orthogonal directions. A crucial constraint imposed on the equilibrium solution is that |Γ(θ∗)|≤π, where |Γ(θ∗)| represents the length of the shortest arc on the unit circle that contains the equilibrium solution θ∗. We provide a proof that there exists a unique solution satisfying the aforementioned stability criteria. This analysis enhances our understanding of the stability and uniqueness of these solutions, offering valuable insights into the dynamics of coupled oscillators in this system.
    Àrees temàtiques: Statistical and nonlinear physics Physics, mathematical Physics and astronomy (miscellaneous) Physics and astronomy (all) Medicine (miscellaneous) Medicina veterinaria Medicina ii Mathematics, applied Mathematical physics Matemática / probabilidade e estatística Interdisciplinar Geociências General physics and astronomy Engenharias iv Engenharias iii Engenharias ii Engenharias i Ciências ambientais Ciência da computação Astronomia / física Applied mathematics
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: sergio.gomez@urv.cat antonio.garijo@urv.cat alexandre.arenas@urv.cat
    Identificador de l'autor: 0000-0003-1820-0062 0000-0002-1503-7514 0000-0003-0937-0334
    Data d'alta del registre: 2024-08-03
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://pubs.aip.org/aip/cha/article/33/9/093127/2911850/On-the-number-of-stable-solutions-in-the-Kuramoto
    Programa de finançament: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Referència a l'article segons font original: Chaos. 33 (9): 093127-
    Referència de l'ítem segons les normes APA: Arenas, Alex; Garijo, Antonio; Gomez, Sergio; Villadelprat, Jordi (2023). On the number of stable solutions in the Kuramoto model. Chaos, 33(9), 093127-. DOI: 10.1063/5.0161977
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acrònim: ATBiD
    DOI de l'article: 10.1063/5.0161977
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2023
    Acció del programa de finançament: Proyectos I+D Generación de Conocimiento
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Applied Mathematics,Mathematical Physics,Mathematics, Applied,Medicine (Miscellaneous),Physics and Astronomy (Miscellaneous),Physics, Mathematical,Statistical and Nonlinear Physics
    Statistical and nonlinear physics
    Physics, mathematical
    Physics and astronomy (miscellaneous)
    Physics and astronomy (all)
    Medicine (miscellaneous)
    Medicina veterinaria
    Medicina ii
    Mathematics, applied
    Mathematical physics
    Matemática / probabilidade e estatística
    Interdisciplinar
    Geociências
    General physics and astronomy
    Engenharias iv
    Engenharias iii
    Engenharias ii
    Engenharias i
    Ciências ambientais
    Ciência da computação
    Astronomia / física
    Applied mathematics
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