Question

Exercise 4. (24 pts.) (Orbit Diagram) Use the Matlab file \"logisticorbit.m\" to plot the orbit diagram for the Logistic map. Change the previous file as needed to plot the orbit diagram for each of the following maps. Make sure to use a large enough range of the parameter value $r$ to obtain the main features of interest. Additionally, run the code a few times to make sure that the chosen initial values do not change your plot (Does your plot change if you run the code more than once?). $\bullet x_{n+1} = x_n e^{-r(1-x_n)}$ (Standard Period Doubling route to chaos) $\bullet x_{n+1} = x_n e^{-rx_n}$ (Only one period Doubling) $\bullet x_{n+1} = r \cos x_n$ (Period Doubling and then chaos) $\bullet x_{n+1} = r \tan x_n$ (Very messy) $\bullet x_{n+1} = rx_n - x_n^3$ (Attractors are sometime symmetric)

          Exercise 4. (24 pts.) (Orbit Diagram) Use the Matlab file \"logisticorbit.m\" to plot the
orbit diagram for the Logistic map.
Change the previous file as needed to plot the orbit diagram for each of the following maps.
Make sure to use a large enough range of the parameter value $r$ to obtain the main features
of interest. Additionally, run the code a few times to make sure that the chosen initial values
do not change your plot (Does your plot change if you run the code more than once?).
$\bullet x_{n+1} = x_n e^{-r(1-x_n)}$ (Standard Period Doubling route to chaos)
$\bullet x_{n+1} = x_n e^{-rx_n}$ (Only one period Doubling)
$\bullet x_{n+1} = r \cos x_n$ (Period Doubling and then chaos)
$\bullet x_{n+1} = r \tan x_n$ (Very messy)
$\bullet x_{n+1} = rx_n - x_n^3$ (Attractors are sometime symmetric)

Exercise 4. (24 pts.) (Orbit Diagram) Use the Matlab file l̈ogisticorbit.mẗo plot the
orbit diagram for the Logistic map.
Change the previous file as needed to plot the orbit diagram for each of the following maps.
Make sure to use a large enough range of the parameter value r to obtain the main features
of interest. Additionally, run the code a few times to make sure that the chosen initial values
do not change your plot (Does your plot change if you run the code more than once?).
∙ xn+1 = xn e^-r(1-xn) (Standard Period Doubling route to chaos)
∙ xn+1 = xn e^-rxn (Only one period Doubling)
∙ xn+1 = r cos xn (Period Doubling and then chaos)
∙ xn+1 = r tan xn (Very messy)
∙ xn+1 = rxn - xn^3 (Attractors are sometime symmetric)

Added by Paul G.

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