The
bifurcation diagram in Figure 12 was realized as follows.
The
bifurcation diagrams and phase portraits of (17) are shown in Figure 3.
Caption: Figure 11:
Bifurcation diagram of system (2) with a = 0.0000001.
Thus, based on the
bifurcation diagram, the waveform, phase portraits, and the power spectrum are utilized to further verify the existence of the chaotic and periodic motion of the blade.
In Figure 3, we firstly fix b = 3 and plot the
bifurcation diagram with respect to a and the related largest Lyapunov exponent.
The Lyapunov exponent spectrum of system in (1) varying with initial condition [l.sub.1] = [w.sub.1o] is shown in Figure 4(a), and the corresponding
bifurcation diagram for y(t) is illustrated as Figure 4(b) with [l.sub.1] [euro] [-5, 5].
Caption: Figure 5:
Bifurcation diagram for illustrating the coexistence of disconnected chaotic attractors with a pair of period-2 limit cycle.
Caption: FIGURE 3:
Bifurcation diagram of Rossler system for [[beta].sub.1] = [[beta].sub.2] = 0.2 using (a) Poincare map and (b) largest Lyapunov exponent.
Caption: Figure 8:
Bifurcation diagram for the system when the amplitude of the road excitation, [??], is 0.05 m: (a) [OMEGA] = 7.96 rad/s to 40 rad/s, (b) [OMEGA] = 7.96 rad/s to 8.25 rad/s.
We see that once [lambda] increases beyond a certain value, the
bifurcation diagram predicts multiple solution.