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Use *XPPAUT *to study the map

*x*_{n+1} = *r x*_{n} *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
to replace the right hand
side. Fill it in as
and click on
.
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*

*1999-09-17*