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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:
where a and are parameters. For this exercise we shall fix and
throughout.
a Set up a function, which given a and returns and according
to the Duffing map.
b Starting from the initial condition and plot the first
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:
d Represent the output of the first iterations of the map on the plane, so
you can see the strange attractor. Remove transient effects by plotting only after iterations.
e Let's look at the fractallike behaviour of the strange attractor. Run your map for many iterations say up to 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 and yin If you run in interactive mode you will be able to zoom in Describe the strange attractor. Is it selfsimilar?
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