Top left: DHO fits of S82 quasars in the ξ, ω ₀ space (LHS of Equation (3)). Underdamped DHOs are located to the left of the solid vertical line (ξ = 1), and overdamped DHOs are located to the right of this same line. The dashed–dotted line further (empirically) separates underdamped DHOs into QPOs and oscillatory DHOs. Both underdamped and overdamped DHOs are colored by their decorrelation timescales (τ _decorr) but using two different color maps. The purple dotted lines on the underdamped population show the evolution of τ _rise across the parameter space, where the numbers give the τ _rise in the unit of days. Top right: DHO fits of S82 quasars in the σ _ϵ , τ _perturb space (RHS of Equation (3)). Same as in the top left panel, colors show the corresponding τ _decorr for each object, and different color maps are used for the underdamped and overdamped populations. Bottom left: the driving process (RHS of Equation (3)) PSDs of the three selected points A, B, and C shown in the top two panels (see footnote 11). Bottom middle: the response functions (LHS of Equation (3)) due to a delta function impulse of the dynamical systems described by the same selected points A, B, and C. Bottom right: DHO light curves simulated using A, B, and C as the input model parameters. Superimposed are the versions down-sampled using the best (magenta) and the worst (orange) cadences of our SDSS light curves (in terms of the number of observations, baseline duration, and photometric accuracy) for each classification. Median photometric uncertainties are used for error bars.