Explosive synchronization in complex networks

Author(s)

Thomas Kauê Dal'Maso Peron

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 2013-02-21

Examining board members

Francisco Aparecido Rodrigues; Rita Maria Cunha de Almeida; Alexandre Diehl

• Advisor: Francisco Aparecido Rodrigues

Abstract

Synchronization processes are observed in many physical, biological, chemical, technological and social systems. These systems can be described and modelled through the theory of complex networks, in a way that the full comprehension of the emergence of collective behavior in these complex systems will only be achieved by theories that encompass the interaction of its elements. In this thesis, we study the emergence of first-order phase transitions in the synchronization of oscillators coupled through heterogeneous and non-trivial structures. By using mean-field theories, we obtain an analytical expression for the critical coupling necessary for the occurrence of explosive synchronization in scale-free networks. Furthermore, we study the behavior of such transitions in the presence of time delays, verifying that is possible to enhance the synchronization level of the oscillators when the interaction is non-instantaneous. The obtained results contribute for the better understanding of the interplay between topology and dynamics in networks. (AU)

• FAPESP's process: 11/02601-6 - Optimization in complex networks
• Grantee: Thomas Kaue Dal Maso Peron
• Support Opportunities: Scholarships in Brazil - Master