  Power grid networks, as well as neuronal networks with synaptic plasticity,
describe real-world systems of tremendous importance for our daily life. The
investigation of these seemingly unrelated types of dynamical networks has
attracted increasing attention over the last decade. In this paper, we provide
insight into the fundamental relation between these two types of networks. For
this, we consider well-established models based on phase oscillators and show
their intimate relation. In particular, we prove that phase oscillator models
with inertia can be viewed as a particular class of adaptive networks. This
relation holds even for more general classes of power grid models that include
voltage dynamics. As an immediate consequence of this relation, we find a novel
type of multicluster state for phase oscillators with inertia. Moreover, the
phenomenon of cascading line failure in power grids is translated into an
adaptive neuronal network.
