  It is a fundamental challenge to understand how the function of a network is
related to its structural organization. Adaptive dynamical networks represent a
broad class of systems that can change their connectivity over time depending
on their dynamical state. The most important feature of such systems is that
their function depends on their structure and vice versa. While the properties
of static networks have been extensively investigated in the past, the study of
adaptive networks is much more challenging. Moreover, adaptive dynamical
networks are of tremendous importance for various application fields, in
particular, for the models for neuronal synaptic plasticity, adaptive networks
in chemical, epidemic, biological, transport, and social systems, to name a
few. In this review, we provide a detailed description of adaptive dynamical
networks, show their applications in various areas of research, highlight their
dynamical features and describe the arising dynamical phenomena, and give an
overview of the available mathematical methods developed for understanding
adaptive dynamical networks.
