  Self-organized network dynamics prevails for systems across physics, biology
and engineering. How external signals generate distributed responses in
networked systems fundamentally underlies their function, yet is far from fully
understood. Here we analyze the dynamic response patterns of oscillatory
networks to fluctuating input signals. We disentangle the impact of the signal
distribution across the network, the signals' frequency contents and the
network topology. We analytically derive qualitatively different dynamic
response patterns and find three frequency regimes: homogeneous responses at
low frequencies, topology-dependent resonances at intermediate frequencies, and
localized responses at high frequencies. The theory faithfully predicts the
network-wide collective responses to regular and irregular, localized and
distributed simulated signals, as well as to real input signals to power grids
recorded from renewable-energy supplies. These results not only provide general
insights into the formation of dynamic response patterns in networked systems
but also suggest regime- and topology-specific design principles underlying
network function.
