Author, as appears in the article.: Arenas, Alex; Garijo, Antonio; Gomez, Sergio; Villadelprat, Jordi
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Arenas Moreno, Alejandro / Garijo Real, Antonio / Gómez Jiménez, Sergio / Villadelprat Yagüe, Jordi
Abstract: 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.
Thematic Areas: 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
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: sergio.gomez@urv.cat antonio.garijo@urv.cat alexandre.arenas@urv.cat
Author identifier: 0000-0003-1820-0062 0000-0002-1503-7514 0000-0003-0937-0334
Record's date: 2024-08-03
Papper version: info:eu-repo/semantics/publishedVersion
Link to the original source: https://pubs.aip.org/aip/cha/article/33/9/093127/2911850/On-the-number-of-stable-solutions-in-the-Kuramoto
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Chaos. 33 (9): 093127-
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
Article's DOI: 10.1063/5.0161977
Entity: Universitat Rovira i Virgili
Journal publication year: 2023
Publication Type: Journal Publications