bifurcation diagram


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bifurcation diagram

A graphical depiction of the relationship between the values of one parameter and the behaviour of the system in which the parameter is being measured.

An example of a bifurcation diagramme is one produced for a logistic map—the x-axis represents all the values of k and the y-axis being all the possible states in the system; typically, the horizontal axis has the parameter and the vertical axis has some aspect of the solution, such as the norm of the solution, the maximum and/or minimum values of one of the state variables, the frequency of a solution or the average of one of the state variables.
References in periodicals archive ?
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.
When the thickness of the honeycomb core cells changes to 0.0012 m and other parameters are kept the same, the bifurcation diagram with in-plane force changing has been presented in Figure 7.
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.