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Synchronization in the Kuramoto model

Grant number: 11/14066-8
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): October 01, 2011
Effective date (End): April 30, 2012
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Tiago Pereira da Silva
Grantee:Jihad Jamil Amine
Home Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

This project aims to investigate the collective behavior of coupled oscillators using tools of dynamical systems theory. The main focus of theproject is the dynamics of phase oscillators, these oscillators have stable amplitude and admit a description in terms of a variable phase. A weak interaction between the oscillators can adjust their phases and frequencies,affecting only slightly the amplitude. Such adjustment rhythms is the essence of the phenomenon of synchronization. The project is divided into three steps: (i) obtain the Kuramoto model, (ii) emergence of synchronization in the limit many oscillators, (iii) numerical analysis of the synchronization onset.