Dynamical phenomena in complex networks: fundamentals and applications

Abstract

During the last decade, networks with complex topology have become a very powerful approach for understanding large complex systems in various fields of applications ranging from Neuroscience, via Engineering to Sociology and Economy. So far, most studies have concentrated on fixed topology, i.e. were strongly restricted in their applicability. Therefore, we study in this project principles of self-organization in evolving complex networks. To bring them closer to various applications, we will investigate in addition the influence of heterogeneity in the network structure, multiscale time delays and stochasticity. These theoretical studies will be intimately connected with the investigation of experimental and natural dynamical networks of increasing complexity starting from a few coupled lasers, via hybrid networks of neurons to the system Earth. The latter one is a special challenge for the network theory and it will be a focus of this project. A main topic will be the understanding of the functioning of the Earth’s subsystems under changing conditions, especially global warming and deforestation in Amazonia. This project is a Brazilian-German international collaborative initiative that engages researches from Instituto Nacional de Pesquisas Espaciais (INPE), Humboldt University at Berlin, Potsdam Institute for Climate Impact Research (PIK) and Universidade de São Paulo (USP). (AU)