Fig. 4. Predicting response patterns of fluctuation-driven networks.
(A) A noisy signal Fi (purple) at one unit and (B) frequency response dθi/dt at another unit in the network (Fig. 1A), with every unit driven by independent Brownian noise. (B) Response prediction (black) is based on 50 dominant Fourier modes of the signal [reconstructing the yellow time series in (A)] at each unit, which, after a transient stage, is very close to the numerical response (purple) to the original signals. (C) Prediction error E (for definition, see Materials and Methods) decreases exponentially with the number of selected Fourier modes. (D) Linear response theory well predicts responses until the maximum line load exceeds 95% (line load Lij ≔ ∣sin(θj − θi)∣), i.e., the system is almost fully loaded at the operating point.