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Use XPPAUT to study the map

xn+1 = r xn e-xn

by copying the old ODE file and replacing the function by
x' = r*x*exp(-x)
Alternately, here is an easier way. Run logistic.ode but click on \fbox{{\tt File}} \fbox{{\tt Edit}} \fbox{{\tt RHS's}} to replace the right hand side. Fill it in as
and click on \fbox{{\tt Ok}}. Change the Window size so that the Yrange is between 0 and 8. Increase r up to 20. For what value of r do you first see period doubling? period 4?

G. Bard Ermentrout