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*XPPAUT *does not do cobwebbing, but you can make it do it by using a
special ODE file that I have created. You are welcome to look at the
file, but I do not include the code here as it is quite
baroque. However, it is instructive to use it. Run it my typing `
xpp cobweb.ode` at the prompt. Before running it, click on
(or tap
)
and fill in the resulting dialog box as
Click on
.
Repeat the above (that is, add a new curve), filling the dialog box
as:
Click on
.
You have added two graphs to the picture on the screen; a plot of
*f*(*x*) vs *x* and a plot of *x* vs *x*, which is just a diagonal
line.
Now click on
(
)
and you
will get a nice cobweb. Change the parameter *r* to 2.95, erase the
screen (
or
), and rerun the simulation. (Either
click on
in the **Parameter Window**, or tap
in the **Main Window**.)
Try *r*=3.1 and *r*=3.5.

Ok, now lets use this cobweb to look at the Ricker model

*x*_{n+1} = *r x*_{n} *e*^{-xn}

To examine this model, you must change three things.
- Change the
function definition. Click on
(
). Change
`F(X)` from `r*x*(1-x)` to `
r*x*exp(-x)` and then click on
.
- Change the dimensions of the window using
and making the X and Y range between 0 and 8. (Change
`X Hi`, `Y Hi` to 8.)
- Change the parameter
`scale` to 8.

Now run the Ricker model with
*r*=5,10,14,18.
For the last cobwebbing example, try the function
with 0<*r*<1, with a window
and `
scale=1`.

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*G. Bard Ermentrout*

*1999-09-17*