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Use Python The Duffing map is defined as follows: x n + 1 = y n , y n + 1 = - b *

Use Python
The Duffing map is defined as follows:
xn+1=yn,yn+1=-b**xn+a**yn-yn3,
where a and b are parameters. For this exercise we shall fix a=2.75 and b=0.2
throughout.
a) Set up a function, which given xn,yn,a and b returns xn+1 and yn+1 according
to the Duffing map.
b) Starting from the initial condition x0=0.5 and y0=0.5, plot the first 400
iterations of the Duffing map.
c) Find the fixed points of the Duffing map. You do not have to do
this numerically.
Type Markdown and LaTeX: 2
d) Represent the output of the first 3000 iterations of the map on the x-y plane, so
you can see the strange attractor. Remove transient effects by plotting only after 100 iterations.
e) Let's look at the fractal-like behaviour of the strange attractor. Run your map for many iterations (say up to 108, but it will depend on your computer). To do this, I recommend setting up a vector to hold all your iteration outputs, and then plotting at the end. This will be much faster than plotting on each time through the loop. Zoom in on a subset of the strange attractor, by plotting only the points that fall in the ranges xin[0.85,1.05] and yin[1.6,1.75]. If you run in interactive mode you will be able to zoom in. Describe the strange attractor. Is it self-similar?

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