Autor según el artículo: Arenas, Alex; Garijo, Antonio; Gomez, Sergio; Villadelprat, Jordi
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: Arenas Moreno, Alejandro / Garijo Real, Antonio / Gómez Jiménez, Sergio / Villadelprat Yagüe, Jordi
Resumen: 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.
Áreas temáticas: 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
Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
Direcció de correo del autor: sergio.gomez@urv.cat antonio.garijo@urv.cat alexandre.arenas@urv.cat
Identificador del autor: 0000-0003-1820-0062 0000-0002-1503-7514 0000-0003-0937-0334
Fecha de alta del registro: 2024-08-03
Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
Enlace a la fuente original: https://pubs.aip.org/aip/cha/article/33/9/093127/2911850/On-the-number-of-stable-solutions-in-the-Kuramoto
URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Chaos. 33 (9): 093127-
Referencia 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
DOI del artículo: 10.1063/5.0161977
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2023
Tipo de publicación: Journal Publications