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tokens: detected oscillatory patterns. Double-peaked emitters 3C 390.3 and Arp 102B Our hybrid method made the distinction between these two objects based on the presence (absence) of underlying periodic variability, despite that the differences in the shapes of their spectral lines are subtle. 2D (auto)correlation maps of Arp 102B have a simple linear shape, but for 3C 390.3 a manifold of substructures is superimposed. Namely, our analysis has shown the fluctuations in the interactions between the oscillations in the continuum and the emission lines of 3C 390.3 due to substantially different levels of correlation polarity. The clusters of correlations are divided by gaps of very low (or no) correlations, and the islands of correlations switch their polarity (between positive and negative values). This can be seen as evidence that there is an activation process that reduces correlation coefficients (from positive values up to zero). Later, a different relationship is evoked between the periodicities in light curves (e.g. negative correlations). The break off of the correlation band (on diagonal) may be due to the change of variability in the light curves or due to the modulatory effects of some unknown background factors, which may have certain cycles. We applied the hybrid method to a series of artificially non-linear and non-stationary oscillatory signals simulated by equations ( 6 ) and ( 12 ) with unidirectional and bidirectional coupling. The degree of non-linearity/asymmetry is controlled by the ratio (differing from 1) of the periods (frequencies) of the sinusoids. To introduce the non-stationary mechanism, we assign a random value between 0 and 10 to the amplitude of signals, while they were fixed over trial realization, adding the red noise. The 2D correlation map of bidirectional coupling of three oscillatory processes (see Fig. 12 ) almost matches the map of the real light curves. Figure 12. Simulation of bidirectional coupled three-oscillator network for the case of 3C 390.3. Left: random realization of equation ( 12 ) from two time series (black is U a = OP 1 and red is U c = OP 2) of amplitudes A = 1.954, B = 1.729, C = 2.357, phase φ = φ 1 = 2.359 rad, coupling strengths cp a → b = 0.7, cp a → c = 0.5, cp b → a = 0.2, cp c → a = 0.3, frequencies f a = 1/1000, f b = 1/300, f c = 1/100, and time delay of 100 arbitrary chosen time units. Right: corresponding 2D correlation map, which clearly shows three clusters related to fundamental periods as well as clusters of negative correlation. We cannot produce a correlation image with negative ‘correlation islands’ if the time delays between processes are different. We note that time delays between the continuum and the Hα and Hβ lines are ∼120 and 95 d, respectively, as reported by Shapovalova et al. ( 2010a ). Based on this, one can see the importance of the value of the time lag for the expression of a negative link between oscillations, which implies that physical places of oscillation