Time evolution of the m = 2,4,1, and 3 (top to bottom) power spectra for the gSa model. The vertical axis shows the frequency, ω = mΩ (in units of km s^-1 kpc^-1), rather than the pattern speed Ω, as done in Fig. 9, in order to facilitate a discussion of coupling between different modes. Time outputs are every 150 Myr with a time window Δt = 300 Myr. Contour levels are normalized for each multiplicity to better follow the changes in amplitude. The orange curves show the resonant loci as in Fig. 9. It is clear that the outer m = 2 wave has a stable pattern speed (slowly decreasing as the bar slows down) for over 600 Myr, while slowly weakening and extending outward with time. In contrast, the inner m = 2 wave bounces between the bar and the outer one at the beat frequency of the latter two patterns. The m = 3 waves are also present for the entire time, shifting outwards with time and largely coinciding in radius with the m = 1 features.