  We investigate topological and spectral properties of models of European and
US-American power grids and of paradigmatic network models as well as their
implications for the synchronization dynamics of phase oscillators with
heterogeneous natural frequencies. We employ the complex-valued order parameter
--~a widely-used indicator for phase ordering~-- to assess the synchronization
dynamics and observe the order parameter to exhibit either constant or periodic
or non-periodic, possibly chaotic temporal evolutions for a given coupling
strength but depending on initial conditions and the systems' disorder.
Interestingly, both topological and spectral characteristics of the power grids
point to a diminished capability of these networks to support a temporarily
stable synchronization dynamics. We find non-trivial commonalities between the
synchronization dynamics of oscillators on seemingly opposing topologies.
