Suppose that r $=2\mathrm{.}75$ and x$0=0\mathrm{.}2.$ Calculate the first hundred iterates, xn$+1=$ rxn$(1$ xn$),$ and

save it as a row vector named A$11.$

Now here comes the hard part: in a separate file or command window $($for MATLAB$)/$console

$($for Python$)$ plot the timeseries $($iteration number $[1,2,...,100]$ vs iterates $[$x$0,$ x$1,...,$ x$99]).$ We can

visually analyze the behavior of the map from the timeseries plot: it is either going to converge to a

fixed point $($called a $$sink$),$ bounce between the same two $($or several$)$ points $($called $$periodic$),$ or

behave in a seemingly random manner $($called $$chaotic$).$

After you observe the plot, come back to your solution file and save the variable behavior as

behavior $=1$ if there appears to be a sink, behavior $=2$ if there appears to be a periodic orbit, or

behavior $=3$ if it appears to be chaotic. We can also analyze this more quantitatively by looking at

the distribution of iterates: the more disordered the iterates become the more its topological entropy

rises. Calculate the standard deviation of the iterates using the function x$\_$std $=$ std$($x$)$ on MATLAB

or x$\_$std $=$ np$.$std$($x$)$ on Python. Save the variable A$12$ as a row vector $[$xstd$,$ behavior$]$