Fig. 3: Analysis of the oscillators’ motions.
From: Synchronization of non-weakly coupled aeroelastic oscillators
The experimentally measured displacements of the oscillators are shown in the time domain (a–c), frequency domain (d–f), toroidal phase space θ1,2 = ω1,2t + ϕ1,2 and its respective Poincaré map θ1p(k) = θ1(tk),  θ2p(k) = θ2(tk) = 2πk (g–i). For large frequency mismatch (dashed line in Fig. 2), the coupling effect is negligible, and oscillators run freely (a, d, g) with a small mutual injection of motion that can only be detected in the power spectra on dB scales. For moderate frequency mismatch (dotted line in Fig. 2), the coupling-induced injected motion pulls the oscillators (b, e, h) toward synchronization. This injection pulling is highly visible both in time (beating envelopes) and frequency (side-bands with a spacing of the beats frequency) domains. For small frequency mismatch (dashed-dotted line in Fig. 2), the oscillators synchronized (c, f, i). The phase-locked synchronized motion is readily identified in the time and frequency domains, and associated with a unique trajectory in the toroidal phase space and a single fixed point in the Poincaré map.
