Figure 3.

(a) Two trajectories converging to the slowest two-dimensional SSM of the oscillator chain. (b,c) Instantaneous damping and frequency curves constructed from a phase space embedding with perfect SSM initialization, from a delay embedding with perfect SSM initialization and from a phase space embedding with imperfect SSM initialization. (d) Decaying trajectories from the slow four-dimensional SSM $\mathcal{W}(E_S^4)$ of the oscillator chain. (e) Test trajectory and its model-based prediction in the normal form domain. (f,g) Instantaneous frequencies of the slow (mode $1$) and fast ($2$) modes of $\mathcal{W}(E_S^4)$. (h,i) Frequency response curve (FRC) and backbone curves predictions from the reduced-order models (3.2) and (3.3) along with forced steady states (dots) obtained via numerical integration of the full system. (Online version in colour.)