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.
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We see that once [lambda] increases beyond a certain value, the bifurcation diagram predicts multiple solution.
By introducing the nonlinear feedback controller, using 4-5 order variable step Runge-Kutta method to carry on the numerical simulation, the bifurcation diagram of the control system is shown in Fig.
Caption: Figure 1: (a) Bifurcation diagram of model (5) with bifurcation parameter r covering [1.
As for bifurcation diagram 4, the corresponding waveform and phase diagrams are gained when the external excitation amplitudes are 2500, 3100, 3300, 3400, 3700, and 3800 N/[m.
Caption: Figure 9: The bifurcation diagram of advertising and retail prices with the change of [k.
To summarize, equation (1) can output (1) a specific pair of D and S time courses (representing a measurable system), or (2) many related time courses forming a phase plane, and (3) many related phase planes forming a bifurcation diagram.
During the study, possible roles of small parameter changes of sample arc furnace system around bifurcation points have been traced over time series analysis, phase plane analysis and bifurcation diagrams.
Bifurcation diagram showing the stability or instability of the system depending on the parameter can be obtained after a series of simulations during which all parameters remaining constant (there is only change of the examined parameter in the desired range).
35, as is evident in the bifurcation diagram [ILLUSTRATION FOR FIGURE 3A OMITTED].
Under the adiabatic condition, the bifurcation diagram for the two-cell model is drawn in Fig.
Figure 3 is a bifurcation diagram for [Mathematical Expression Omitted] based on parameters [Mu] = 0.
Figure 4 presents bifurcation diagram and the corresponding largest Lyapunov exponents with respect to [[alpha].