1) I am trying to plot the Basin of attraction for 2d discrete dynamical system in MATLAB. Please give some suggestions to get them.
2) If possible, give some simple example like x(n+1)=…..y(n+1)=…. which has two fixed points.
3) Idea is, took different initial conditions and separate them with different color in which they approach to the two fixed points.
one possible method is writing down the fixed points explicitly, for x0 in a range, and nestling for y0, iterate the system forward, if the iterates approach one fixed points, then mark the points (x0,y0) with 1 or the other number, if the iterates approach to the other points, mark the initial points with a different number, and break the nested for if y0 ends its interval. then begin the next x0 with a new block,.nested y0 again as before, and so on, until the for for x0 ends its interval.
Thank you Xian-Feng Li sir,
1) I did as you answered above, for the flows. I got it. Thank you for your answer. But when I tried on maps, its need lot of iteration process to converge to the fixed points, it took lot of time.
2) Its there any tool to plot Basin of attraction.
3) If it possible, please share some references. I will go through it.
Matlab becomes very slow for nested fors. One way is to use vector. Another ways is to use effective languages, e.g., C/C++, Python, et al. Matlab has its parallel toolbox, I tried before, it is not suitable for nested fors.
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