The Forced Van der Pol equation (FVDP) Cornell Mathematics REU 2002

Professors John Guckenheimer Professor Guckenheimer and Warren Weckessar's Professor Weckessar's Cornell Page Group
I, Sabyasachi Guharay, along with four other students have been working with Professors Guckenheimer and Weckessar during this summer on the FVDP. I present some of my main work and programs on this website. For more details contact me via email.
Sabyasachi's Notes
• Here is introductory part of my talk (I believe provides a succint introduction to the FVDP) intro.ps
• research.ps Here are the slidesfrom the research part of my final presentation to the REU
• finalslides.tar.gz Slides from my final presentation to the REU
• mathfesttalk.ps Here are the slides that I presented at MathFest 2002
Perl, Matlab and UNIX Scripts which I used routinely
• stuffextract.pl
This file extracts the necessary information from the solutions file of the AUTO run. NOTE: DO NOT USE THIS PROGRAM FOR EXTRACTING INFORMATION FROM JACOBIAN CALCULATIONS. USE ONLY WHEN EXTRACTING Y_0, Phi_0, Y_FINAL and Phi_FINAL. Syntax: (perl extractstuff.pl s.filename >! outfile)
• extractjacobian.pl
This is a similar program to stuffextract.pl. The difference is that one should use this program when one has used AUTO to compute the jacobian values. NOTE: USE THIS PROGRAM FOR JACOBIAN CALCULATED OUTPUT: USE WHEN EXTRACTING Y_O, Phi_0, Y_FINAL, Phi_FINAL and DXDY_0, etc. This outputs the following: Y_O, Phi_0, Y_FINAL, Phi_FINAL, DxDy_FINAL, DxDtheta_FINAL, DyDy_FINAL and DyDtheta_FINAL. Syntax (perl extractjacobian s.filename >! outfile)
• printmap.m
This is a Matlab script which inputs the output file from the above Perl script and makes the nice Horse-shoe plot
• sorted_sizes
Since AUTO runs get large, one can use this unix script to check where the large files are (run from home directory) Syntax (sorted_sizes >! outfile)
For other Matlab related programs please go here: Professor Weckessar's Website

AUTO calculations
• HowtoRun
This is more or less a README type of file which gives in depth instructions on how to run the AUTO calculations of finding a horse-shoe.
• NewAutoScript
This is a small script which one can use to run the AUTO calculations from a single command line. However one needs to edit the parameters in this file. To run this, you should delete all lines beginning with #. You should run a script similar to this (with your filenames) after you have made the constants file, the c file and starting data point file. to run the above script see direction 7) in HowtoRun file. To see a more generic case, look at the next program.
• GenericScript
This is a generic script for running the AUTO calculations from a single command line. NOTE: Neither this nor the above file will work. You need to put in your own filenames.
• Sample Constants File for AUTO
Here is sample file of how the constants file should look like. Short explanations of pertinent constants:
• IRS = label you are starting at;
• NTST
= number of divisions in grid (bigger, then finer;
• NMX
= number of steps to make;
• RL0
= lower bound of area searched;
• RL1
= upper bound;
• NPR
= make label ever NPRth step;
• DS
= starting step size;
• DSMIN
= smallest step size;
• DSMAX
= largest step size;
• NUZR
= how many points do you want to specify for labels?;
• NDIM
= no. of dimension (3 for FVDP);
• NBC
x= no. of boundary conditions (4 for FVDP); DS, RLO, RL1, IRS are the main objects that you may need to change.
• Sample C File for AUTO
Here is sample file of how the c file should look like. We show here the case for the forced van der Pol equation.
• Sample Starting data file for AUTO
Here is sample file of how the starting data file should look like.
• Actual output given by AUTO
• Sample output files from AUTO runs of above
• b.fvdpmap
• d.fvdpmap
• s.fvdpmap
• Main AUTO files used in research
• c.fvdpmap3
This is the constants file for the following parameters: epsilon = 0.0001 a = 1.1 omega = 1.55 y0 = -0.7 phi0 = 2.26194671058465
• fvdpmap3.c
The C file for the FVDP with the above parameters and with initial conditions such as x(0) = -1 and x(1) = 1.
• fvdpmap3.dat
Starting data file for the above case.
• c.fvdpmap4
This is the constants file for the following parameters: epsilon = 0.0001 a = 1.1 omega = 1.55 y0 = -0.63 phi0 = 2.26194671058465
• fvdpmap4.c
The C file for the FVDP with the above parameters and with initial conditions such as x(0) = -1 and x(1) = 1.
• fvdpmap4.dat
Starting data file for the above case.
• The next set of files are for when we varied epsilon (not Phi) for the Jacobian calculations