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Next: Homework Up: No Title Previous: Entering an equation

Running a simulation

Once you have enetered an ODE file, you can run XPPAUT on it with the command (it varies from system to system). To run XPPAUT in UNIX type xpp logistic.ode at the command line. In Winpp, click on the Winpp icon and load the equation. I have assumed you have named the file logistic.ode.

If everything was typed correctly, a main window and several other windows appear. Three of these other windows are of interest:

Note: If any of the windows appear ``dead'', then iconify them and reopen them. This happens on some window managers.

The Main Windowhas all the menus etc and the one we will work from the most.

Click on \fbox{{\tt Initialconds}} and then \fbox{{\tt Go}} or tap \fbox{{\bf i}} \fbox{{\bf g}} and the equations will be iterated for 200 steps. Click on \fbox{{\tt Window}} \fbox{{\tt window}} ot tap \fbox{{\bf w}} \fbox{{\bf w}} to change the window size. Fill in as follows

\fbox{\begin{tabular}{ll\vert ll }
\par {\tt X Lo:}& 0 & {\tt Y Lo:} & 0 \\
\hline
{\tt X Hi:}& 200 & {\tt Y Hi:}& 1
\end{tabular}}
and click on \fbox{{\tt Ok}} or tap \fbox{{\bf Tab}} to accept the values.

In the Initial Data Window, change the initial value to .01 and click on \fbox{{\tt Go}}.

Change the parameter r from 2.5 to 3.2 in the parameter window and click on \fbox{{\tt Go}}. Note that you have a period 2 solution. This may be hard to see with this many points. Rewindow to expand around a small region, for example

\fbox{\begin{tabular}{ll\vert ll }
\par {\tt X Lo:}& 50 & {\tt Y Lo:} & 0 \\
\hline
{\tt X Hi:}& 100 & {\tt Y Hi:}& 1
\end{tabular}}

Now change r to 3.5. Click on \fbox{{\tt Erase}} or tap \fbox{{\bf e}} to clear the window and click on either \fbox{{\tt Go}} in the Parameter Windowor tap \fbox{{\bf i}} \fbox{{\bf g}} in the Main Window. What do you see now? A period 4 solution should be clearly evident. Choose r=3.75 and look again. You might want to make the window cover more iterates.

Exit the simulation now by clicking on \fbox{{\tt File}} \fbox{{\tt Quit}} \fbox{{\tt Yes}}.


 
next up previous
Next: Homework Up: No Title Previous: Entering an equation
G. Bard Ermentrout
1999-09-17