Self-organization in continuous adaptive networks von der Fakultät für Mathematik und

Complex systems of coupled dynamical units can often be understood as adaptive networks. In such networks the dynamical exchange of information between the local and topological degrees of freedom gives rise to a plethora of self-organization phenomena. Analytical studies can elucidate the mechanisms behind these phe-nomena. The development of respective approaches, however, is impeded by the necessity to capture both, the dynamical as well as structural aspects of the network. This work explores a new analytical approach, which combines tools from dynam-ical systems theory with tools from graph theory to account for the dual nature of adaptive networks. To our knowledge, it is the first approach that is applicable to continuous networks. We use it to study the mechanisms behind three emergent phenomena that are prominently discussed in the context of biological and social sciences: synchronization, spontaneous diversification, and self-organized critical-ity. First, we analyze the relation between structure and dynamics in a network of cou