Adaptive dynamical networks is a general modeling paradigm that occurs in almost all application areas. Probably the best known example of adaptive networks are neural networks with plasticity, which change their structure during the learning phase. Other examples are adaptive epidemiological networks, transport networks or power grids. I will introduce adaptive dynamical networks with slow adaptation and their basic properties. In particular, I will explain how adaptivity leads to the emergence of phenomena such as hierarchical clusters, recurrent synchronization, or resistance to desynchronizing effects of noise.
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