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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Instantaneous frequencies in the Kuramoto model

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da Fonseca, Julio D. [1] ; Leonel, Edson D. [1] ; Chate, Hugues [2, 3, 4]
Total Authors: 3
[1] Univ Estadual Paulista, Dept Fis, BR-13506900 Rio Claro, SP - Brazil
[2] Univ Paris Saclay, Serv Phys Etat Condense, CEA Saclay, CEA, CNRS, F-91191 Gif Sur Yvette - France
[3] Computat Sci Res Ctr, Beijing 100193 - Peoples R China
[4] Sorbonne Univ, Lab Phys Theor Mat Condensee, CNRS, F-75005 Paris - France
Total Affiliations: 4
Document type: Journal article
Source: Physical Review E; v. 102, n. 5 NOV 23 2020.
Web of Science Citations: 0

Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical description of the instantaneous frequency (phase-velocity) distribution. Our result is validated against numerical simulations, and we illustrate it in cases in which the natural frequencies have normal and Beta distributions. In both cases, we vary the coupling strength and compare systematically the distribution of time-averaged frequencies (a known result of Kuramoto theory) to that of instantaneous frequencies, focusing on their qualitative differences near the synchronized frequency and in their tails. For a class of natural frequency distributions with power-law tails, which includes the Cauchy-Lorentz distribution, we analyze the tails of the instantaneous frequency distribution by means of an asymptotic formula obtained from a power-series expansion. (AU)

FAPESP's process: 19/14038-6 - Investigation of dynamical properties in nonlinear systems
Grantee:Edson Denis Leonel
Support Opportunities: Regular Research Grants
FAPESP's process: 19/12930-9 - Statistical properties of instantaneous frequencies in the Kuramoto model
Grantee:Julio César David da Fonseca
Support Opportunities: Scholarships in Brazil - Post-Doctoral