Modelling of dynamical processes in complex networks

Abstract

Complex systems are composed by discrete parts that interact non-linearly and can be represented as complex networks. The analysis of such systems is fundamental for the study of the brain, of society, the Internet, the World Wide Web and food webs. In this project, we propose to complement the works related to the analysis of the influence of the organization of complex networks in the evolution of dynamic processes. We will analyze how the presence of third order cycles influences the spectrum of networks, which is directly related to dynamic processes, such as synchronization and epidemic spreading. We will complement the studies related to the process of explosive synchronization in complex networks, in order to determine how local properties of oscillators lead to the emergence of this phenomenon. Dynamic processes will be analyzed in spatial networks, to determine how the spatial properties interfere in such processes. Models of rumors spreading based on Markov chains will be developed and we will investigate how regression methods can be used to predict the evolution of social dynamics. Finally, we will determine how patterns of connections influence dynamic processes using data mining tools. These studies will quantify how the organization of different complex systems affects dynamic processes, to enable a better understanding of the relationship between structure and dynamics of networks. (AU)