  Multistability is a common phenomenon which naturally occurs in complex
networks. If coexisting attractors are numerous and their basins of attraction
are complexly interwoven, the long-term response to a perturbation can be
highly uncertain. We examine the uncertainty in the outcome of perturbations to
the synchronous state in a Kuramoto-like representation of the British power
grid. Based on local basin landscapes which correspond to single-node
perturbations, we demonstrate that the uncertainty shows strong spatial
variability. While perturbations at many nodes only allow for a few outcomes,
other local landscapes show extreme complexity with more than a hundred basins.
Particularly complex domains in the latter can be related to unstable invariant
chaotic sets of saddle type. Most importantly, we show that the characteristic
dynamics on these chaotic saddles can be associated with certain topological
structures of the network. We find that one particular tree-like substructure
allows for the chaotic response to perturbations at nodes in the north of Great
Britain. The interplay with other peripheral motifs increases the uncertainty
in the system response even further.
