Figure 5.

(a) Bifurcation diagram for the dimensionless ODEs at P_ee=548.066. The parameter Γ_e is varied and the stable (solid lines) and unstable (dashed line) fixed points in h_e are shown. The asterisks denote the two Hopf bifurcations. The dash–dot lines denote the maximum and minimum values of h_e achieved during a stable limit cycle. The dotted lines denote the maximum and minimum values of h_e achieved during an unstable limit cycle. The branch of limit cycles is born and dies in two subcritical Hopf bifurcations; two saddle–node bifurcations of limit cycles lead to large-amplitude stable oscillations with sudden onset. (b) Numerical solution to the dimensionless ODEs at Γ_e=0.96×10⁻³ and P_ee=548.066, near the rightmost Hopf bifurcation in (a). Dimensional h_e is plotted as a function of dimensional time t. The oscillations in h_e occur at a frequency near 7.5 Hz and are stable to perturbations.