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Statistical properties of instantaneous frequencies in the Kuramoto model

Grant number: 19/12930-9
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): September 01, 2019
Effective date (End): August 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal Investigator:Edson Denis Leonel
Grantee:Julio César David da Fonseca
Home Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This project consists in investigating the statistical distribution of instantaneous frequencies in the Kuramoto model. Our main goal is to obtain a probability densityfunction which defines this distribution, studying its main properties and validity conditions. We will obtain a relation between the moments of the natural frequencies and themoments of the instantaneous frequencies, analyzing then how the statistical properties ofthe natural frequencies affect the statistical properties of the instantaneous frequencies. During our research work, we will also extend the results obtained in the context of the Kuramotomodel to the Kuramoto-Sakaguchi model. The methods are mainly based on our recentwork devoted to reviewing and interpreting the Kuramoto theoretical approach tothe study of synchronization.