  Recent work found distributed resonances in driven oscillator networks and AC
power grids. The emerging dynamic resonance patterns are highly heterogeneous
and nontrivial, depending jointly on the driving frequency, the interaction
topology of the network and the node or nodes driven. Identifying which nodes
are most susceptible to dynamic driving and may thus make the system as a whole
vulnerable to external input signals, however, remains a challenge. Here we
propose an easy-to-compute Dynamic Vulnerability Index (DVI) for identifying
those nodes that exhibit largest amplitude responses to dynamic driving signals
with given power spectra and thus are most vulnerable. The DVI is based on
linear response theory, as such generic, and enables robust predictions. It
thus shows potential for a wide range of applications across dynamically driven
networks, for instance for identifying the vulnerable nodes in power grids
driven by fluctuating inputs from renewable energy sources and fluctuating
power output to households.
