Figure 7.

Pitchfork bifurcations of period-doubling and period-tripling for stiffness contrasts of μ_l/μ_s = 5 and μ_l/μ_s = 8. Initially, the growing layer is flat and the amplitudes are zero. At first instability point ϑ_w, all amplitudes begin to grow simultaneously. For the case of period-doubling (red curves), at the second instability point ϑ_pd, a pitchfork bifurcation occurs: every second amplitude grows and those in between decay. For the case of period-tripling (blue curves), ϑ_pd is passed without bifurcation. Further growth initiates period-tripling at the secondary bifurcation point ϑ_pt: every third amplitudes grows and those in between decay. The time between primary and secondary bifurcation increases with increasing stiffness contrast μ_l/μ_s.