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 intend to study in this IRTG principles of self-organization in evolving complex networks. To bring these principles closer to various applications, we will in addition investigate 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 lasers, via hybrid networks of neurons to the Earth system. The latter one is a special challenge for the network theory and it will be a focus of this IRTG. In this context, the main topic will be to understand the functioning of the Earth´s subsystems under changing conditions, especially global warming and deforestation in Amazonia.
A key goal of this interdisciplinary IRTG will be to develop a structured PhD program which will enable young researchers to work in network theory as well as across various fields of network applications. It comprises education on modern theoretical concepts and training on network applications, even involving "hands-on" experience with the corresponding experiments. The training program includes dual supervision of each student, annual schools, workshops and on-site learning, but innovative forms of learning and communication such as teleconferences, e-learning, or wikiversity will be extensively used too. Special emphasis will be devoted to soft skills education by making use of the Humboldt Graduate School and the University of Sao Paulo.
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