Several kinds of complex systems can be described in terms of complex networks, for instance, electrical power grids, metabolic networks, Internet and social networks. The mathematical concept of network has recently been turned into an important tool for describing complex systems, whose principal characteristic is that they consist of a large number of mutually interacting dynamical parts which are coupled in a nonlinear fashion. The theory of complex networks attempts to explain the structure of interactions between the subunits of a system in order to understand their functioning and the processes taking place in them. It tries, for instance, to grasp how the structure of social networks affects the spread of information or human diseases or even how the structure of the World Wide Web influences the search engines and surfing behavior. In this project, we will study how the topology influences the emergence of collective behavior in a population of oscillators. More specifically, we will study synchronization processes in networks in which the local topology presents cycles of order three and arbitrary distributions of subgraphs. Moreover, in order to investigate synchronization processes in systems with characteristics more similar to those observed in real systems, we will extend the models in order to include assortativity, noise and delays in the connections. These studies will allow a better comprehension about synchronization in real networks, once the models reported in the literature are based on results derived for the traditional configuration model in the absence of fluctuations and perturbations, which fails to describe the local topology and, consequently, the dynamics of real-world networks.
News published in Agência FAPESP Newsletter about the scholarship: