Science Advances

Supplementary Materials

The PDF file includes:

  • Section S1. Theory of dynamic response patterns in oscillatory networks
  • Section S2. Frequency regimes of dynamic response patterns
  • Section S3. Predicting dynamic responses to irregular and distributed noises
  • Section S4. Limit of validity of linear response theory
  • Fig. S1. Estimating response strength in inhomogeneous networks.
  • Fig. S2. Dynamic network response patterns in three regimes.
  • Fig. S3. Three frequency regimes of response patterns in networks of first-order (Kuramoto) oscillators.
  • Fig. S4. An illustration of the frequency sampling method.
  • Fig. S5. Grid responses to real-world power fluctuations.
  • Fig. S6. Limit of validity of linear response theory under strong perturbations.
  • Fig. S7. Breakdown of linear response theory at the fully loaded point.
  • Fig. S8. Limit of validity of linear response theory in heavily loaded networks.
  • References (3945)

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Other Supplementary Material for this manuscript includes the following:

  • Movie S1 (.mp4 format). Network response to Brownian noise at one node (accompanying Fig. 1).
  • Movie S2 (.mp4 format). Network response to independent Brownian noise at all nodes (accompanying Fig. 4, A and B).
  • Movie S3 (.mp4 format). Network response to a sinusoidal signal in bulk regime (accompanying Fig. 2B).
  • Movie S4 (.mp4 format). Network response to a sinusoidal signal in resonance regime (accompanying Fig. 2C).
  • Movie S5 (.mp4 format). Network response to a sinusoidal signal in localized regime (accompanying Fig. 2D).
  • Movie S6 (.mp4 format). Network response to a real-world wind power fluctuation (accompanying Fig. 5A).
  • Movie S7 (.mp4 format). Network response to a real-world photovoltaic power fluctuation (accompanying Fig. 5B).

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