Chaos them: explore the sequence xn+1 = f(xn) where f(x) =r x(1-x), starting with an initial condition x0 between 0 and 1.
Write the matlab code to construct a cobweb diagram of the sequence. Draw the cobweb diagram for different r and different x0. Try to figure out when "chaos" sets in as r increases. Need to test value of x0 .
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function cobweb(r,x0,N, to_wait)
% r -- the coefficient of f(x)=rx(1-x); r should be in the range of 0 to 4
% x0 -- initial condition (.5 default)
% N -- the number of iterates for which to draw the cobweb (100 default)
% to_wait -- 0 or 1 (0 default)
% 0 -- draw the cobweb straight from the beginning
% 1 -- iterate the point x0 1000 times BEFORE drawing the cobweb N
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