plot the bifurcation into multiple colors on mathematical modelling case

I want to plot bifurcation, this is the result I want. Parameter space Phi × u for Pr = 0.002.

I don't have any idea how to make this. I only have this script (attach)

[Latifah Hanum]

can you help me to change this script?

Answer 1

[Sargondjani]

I dont have time to look into your code, but I usually plot bifurcations using "contour". I compute the eigenvalues, and then define the fieds in the graphs by setting the boundaries of the countour to the bifurcation values. An example of my code:

contour(mm_vec,z1_vec,l1,[1 1],'-k','LineWidth',LW);

contour(mm_vec,z1_vec,l2,[1 1],'-','LineWidth',LW,'Color',[0 0.447 0.741],'HandleVisibility','off');

contour(mm_vec,z1_vec,l3,[1 1],'-b','LineWidth',LW,'HandleVisibility','off');%'Color',[0.85 0.325 0.098]

contour(mm_vec,z1_vec,l1,[-1 -1],'-.k','LineWidth',LW);

contour(mm_vec,z1_vec,l2,[-1 -1],'-.','LineWidth',LW,'Color',[0 0.447 0.741]);

contour(mm_vec,z1_vec,l3,[-1 -1],'-.b','LineWidth',LW,'HandleVisibility','off');%,'Color',[0.85 0.325 0.098]

contour(mm_vec,z1_vec,imag_size,[1e-8 1e-8],':','LineWidth',LW2,'Color',[0.85 0.325 0.098]);%,'fill','on');

In this code mm and z1 are the axis (bifurcation parameters), and l1, l2 and l3 are the eigenvalues, and imag_size is the imaginary part when there exists complex eigenvalues. (Note that these are discrete time bifurcations).

To get smooth plots in case of non-linear graphs your vectors mm and z1 have to be large.