Using MATLAB, how to draw the bifurcation diagram for a chaotic system?
Can you kindly share any *.m file (MATLAB code) for this? How to do this?
Can you illustrate the bifurcation analysis with any classical system like for example, the Lorenz system?
Hi Sundarapandian Vaidyanathan
these links may useful for understanding and producing the matlab code.(.m file).
Research Chaotic dynamics - Rössler system
https://www.mathworks.com/matlabcentral/answers/566973-bifurcation-diagram-for-discrete-system-using-matlab-code
https://www.mathworks.com/matlabcentral/answers/437991-producing-a-bifurcation-diagram-how-to-make-this-code-faster
https://www.mathworks.com/matlabcentral/answers/274508-bifurcation-code-for-delay-lorenz-system
https://en.wikipedia.org/wiki/Logistic_map gives some examples of how to depict a bifurcation diagram. You could, for example, choose a set of random points and make a movie of their dynamical evolution. If you want the actual attractor, that requires an infinite number of steps, so the best you can do (in chaotic regions) is to run it for a very long time. In non-chaotic regions, you can sometimes calculate the curves and draw them directly.
See for example: Patrick Sylvestre-Baron (2021). Plotting bifurcation diagram. (https://www.mathworks.com/matlabcentral/fileexchange/72057-plotting-bifurcation-diagram), MATLAB Central File Exchange. Retrieved September 22, 2021. You can find there as example the Rossler system.
All the best.
Aswer in russian. https://www.youtube.com/watch?v=ph9DpaezUi4
Parameter continuation is a powerful tool to do that. You can use it to study the bifurcation of fixed points and periodic orbits. Further, one can use parameter continuation to obtain stable/unstable manifolds of the dynamical system. There are a few continuation packages, including AUTO, MATCONT, and COCO.
Illustrative video on how to generate the diagram https://www.youtube.com/watch?v=qRshb6V-1ug