  Given a power grid and a transmission (coupling) strength, basin stability is
a measure of synchronization stability for individual nodes. Earlier studies
have focused on the basin stability's dependence of the position of the nodes
in the network for single values of transmission strength. Basin stability
grows from zero to one as transmission strength increases, but often in a
complex, nonmonotonous way. In this study, we investigate the entire functional
form of the basin stability's dependence on transmission strength. To be able
to perform a systematic analysis, we restrict ourselves to small networks. We
scan all isomorphically distinct networks with an equal number of power
producers and consumers of six nodes or less. We find that the shapes of the
basin stability fall into a few, rather well-defined classes, that could be
characterized by the number of edges and the betweenness of the nodes, whereas
other network positional quantities matter less.
