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Typical partial bifurcation diagrams for the first Hopf bifurcation and second Hopf bifurcation. Top and bottom plots represent respectively the maximum amplitude of the periodic oscillation branches and their oscillation frequency with respect to the blowing pressure. Left: case of the first Hopf bifurcation, = 28.67 Hz; right: case of the second Hopf bifurcation, = 51.35 Hz. The line thickness indicates whether the branch portion is stable (thick line) or unstable (thin line). The points H1 and H2 correspond to the Hopf bifurcation points at which a stable oscillation regime arises from the equilibrium for the first and second Hopf bifurcation respectively. S1 and S2 correspond to the saddle-node bifurcation points at which the stable regime arising from the Hopf point destabilises. S1′ and S2′ correspond to the saddle-node bifurcation points at which another stable regime appears for the first and second Hopf bifurcation respectively. S1″ corresponds to the saddle-node bifurcation point at which the stable regime of the pedal note arises from the isolated branch (lime green). (a) First Hopf bifurcation. (b) Second Hopf bifurcation.
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