Synchronization in the Kuramoto Model

• Grant number: 11/14066-8
• Support Opportunities: 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 - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Jihad Jamil Amine
• Host 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.