Fractional radius amplitude for the first overtone (A₁) and for the fundamental mode (A₀) for six consecutive Cepheid models of set R2. The models were initialized with a range of amplitude ratios (bottom left parts of the diagrams) and for each initialization the time evolution (marked with arrow) was followed. The model properties are given in each panel. The proximity to the resonance centre is characterised by Δ = 2ω₁/(ω₀ + ω₂). Solid and open squares mark the location of stable and unstable fixed points computed through fitting the hydrodynamical trajectories with non-resonant amplitude equations. In panels three to five some trajectories evolve to a double-periodic attractor with finite amplitude in both the fundamental and first overtone modes. The remaining (rightmost) trajectories calculated for these three models evolve towards a single-periodic finite amplitude fundamental mode pulsation.