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<!--?xml version="1.0" encoding="UTF-8" ?-->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml"><head>
<meta http-equiv="content-type" content="text/html; charset=windows-1252">
<link rel="stylesheet" type="text/css" media="screen" href="AUTO_files/auto.css">
<meta name="Author" content="Pankaj Kamthan">
<title>AUTO</title>
</head>
<body>
<p class="navigation" align="center">| <a href="#announcements">Announcements</a> | <a href="#introduction">What is AUTO?</a> | <a href="#evolution">Evolution</a> | <a href="#distribution">Distribution</a> | <a href="#documentation">Documentation</a> | <a href="#applications">Applications</a> | <a href="#related_software">Related Software</a>
| <a href="#lecture_notes">Lecture Notes</a> |</p>
<h1 class="title">AUTO<br>
<small>SOFTWARE FOR CONTINUATION AND BIFURCATION PROBLEMS IN ORDINARY DIFFERENTIAL
EQUATIONS</small></h1>
<p>This is the Home Page of the AUTO Web Site, established in January 1996.</p>
<h2><a name="announcements"></a>ANNOUNCEMENTS</h2>
<ul>
<li>[November 28, 2019] Version 0.9.2 of AUTO-07p is available at GitHub.</li>
</ul>
<!--
<ul>
<li>[January 1, 2011] Version 0.8 of AUTO-07p is available at SourceForge.</li>
<li>[December 12, 2008] AUTO-07p demos have been updated.</li>
<li>[August 31, 2007] AUTO-07p has been updated.</li>
<li>[August 27, 2006] AUTO-07p is available.</li>
<li>[March 15, 2006] AUTO 2000 has been updated.</li>
</ul>
-->
<h2><a name="introduction"></a>INTRODUCTION</h2>
<p>AUTO is a software for continuation and bifurcation problems in
ordinary
differential equations, originally developed by Eusebius Doedel, with
subsequent
major contribution by several people, including Alan Champneys, Fabio
Dercole, Thomas Fairgrieve, Yuri Kuznetsov, Bart Oldeman, Randy
Paffenroth, Bjorn Sandstede, Xianjun Wang, and Chenghai Zhang.</p>
<p>AUTO can do a limited bifurcation analysis of algebraic systems of the form </p>
<p align="center">f(u,p) = 0, f,u in <strong>R</strong><sup>n</sup></p>
<p>and of systems of ordinary differential equations of the form </p>
<p align="center">u'(t) = f(u(t),p), f,u in <strong>R</strong><sup>n</sup></p>
<p>subject to initial conditions, boundary conditions, and integral constraints. Here p
denotes one or more parameters. AUTO can also do certain continuation and evolution
computations for parabolic PDEs. It also includes the software HOMCONT for the bifurcation
analysis of homoclinic orbits. AUTO is quite fast and can benefit from multiple
processors; therefore it is applicable to rather large systems of differential
equations.</p>
<p>For further information and details, see the <a href="#documentation">AUTO
Documentation</a>.</p>
<h2><a name="evolution"></a>AUTO STATUS/EVOLUTION</h2>
<p>The following table represents the historical evolution in the development of AUTO in a
chronological order.</p>
<div align="center"><center>
<table width="100%" cellspacing="0" cellpadding="2" border="1">
<tbody><tr>
<th>Year </th>
<th>Version Specification</th>
<th>Affiliation</th>
</tr>
<tr>
<td>1976 </td>
<td>Early program for BVP in ODEs </td>
<td>California Institute of Technology, Pasadena,
USA</td>
</tr>
<tr>
<td>1980 </td>
<td>First distributed version </td>
<td>Concordia University, Montreal, Canada</td>
</tr>
<tr>
<td>1986 </td>
<td>AUTO86 </td>
<td>California Institute of Technology, Pasadena,
USA</td>
</tr>
<tr>
<td>1994 </td>
<td>X/Motif version : AUTO94 </td>
<td>California Institute of Technology, Pasadena,
USA</td>
</tr>
<tr>
<td>1994</td>
<td>Parallel version: AUTO94P </td>
<td>California Institute of Technology, Pasadena,
USA</td>
</tr>
<tr>
<td>1997 </td>
<td>AUTO97, with HOMCONT</td>
<td>Concordia University, Montreal, Canada</td>
</tr>
<tr>
<td>2000</td>
<td>C
Language Version</td>
<td>California Institute of Technology, Pasadena,
USA</td>
</tr>
<tr>
<td>2007</td>
<td>AUTO-07p</td>
<td>Concordia University, Montreal, Canada</td>
</tr>
</tbody></table>
</center></div>
<h2><a name="distribution"></a>AUTO AVAILABILITY/DISTRIBUTION</h2>
<p>The AUTO package is available for UNIX/Linux-based computers. </p>
<h3>AUTO-07P</h3>
<p>AUTO-07p is the successor to both AUTO97 and AUTO2000. </p>
<p>It includes new plotting utilities, namely PyPlaut and Plaut04. It also
contains many of the features of AUTO2000, including the Python CLUI, some
parallelization, dynamic memory allocation, and the ability to use user equation
files written in C. The overall performance has improved, especially for systems
where the Jacobian matrix is sparse.</p>
<p>AUTO-07p is written in
Fortran. At least a Fortran 90 compiler is required to compile AUTO-07p. One
such compiler is the freely downloadable
<a href="http://gcc.gnu.org/wiki/GFortran">GNU Fortran 95 compiler (gfortran)</a>.
Gfortran ships with most current Linux distributions.</p>
<ul>
<li>Distribution:
<a href="https://github.com/auto-07p/auto-07p/releases">Download at GitHub</a>.</li>
</ul>
<!--
<h3>AUTO2000</h3>
<ul>
<li>Distribution:
<a href="http://sourceforge.net/project/showfiles.php?group_id=21781">Download</a> at <a href="http://auto2000.sourceforge.net/">SourceForge</a>.</li>
</ul>
-->
<h2><a name="documentation"></a>AUTO DOCUMENTATION</h2>
<p>The AUTO distribution include a copy of the AUTO Manual in L<small>A</small>T<small>E</small>X,
PostScript, and Portable Document Format (PDF).</p>
<h2><a name="applications"></a>AUTO APPLICATIONS</h2>
<p>AUTO has been used in many scientific and engineering applications. A sample
of applications can be found by searching on the Web for "bifurcation software AUTO".</p>
<h2><a name="related_software"></a>RELATED SOFTWARE</h2>
<p>Other software directly or indirectly related to AUTO includes DSTool,
PyDSTool, XPPAUT, Content, MatCont, and DDE-BifTool.
</p><h2><a name="lecture_notes"></a>RELATED LECTURE NOTES</h2>
<ul>
<li><a href="http://indy.cs.concordia.ca/auto/notes.pdf">Lecture
Notes on Numerical Analysis of Nonlinear Equations</a>. By Eusebius Doedel.
Last Modified: Spring 2010.</li>
</ul>
<!--
<h2>AUTO-07P DEMOS</h2>
<ul>
<li><a href="demos/ab.tar.gz">ab</a>,
<a href="demos/abc.tar.gz">abc</a>,
<a href="demos/bvp.tar.gz">bvp</a>,
<a href="demos/exp.tar.gz">exp</a>,
<a href="demos/fhn.tar.gz">fhn</a>,
<a href="demos/lrz.tar.gz">lrz</a>,
<a href="demos/pp2.tar.gz">pp2</a>,
<a href="demos/pp3.tar.gz">pp3</a>,
<a href="demos/r3b.tar.gz">r3b</a>,
<a href="demos/spb.tar.gz">spb</a>,
<a href="demos/vhb.tar.gz">vhb</a>.</li>
<li><a href="demos/constants.ps">A summary of AUTO constants</a>. [PostScript]</li>
<li><a href="demos/ab-tutorial.zip">ab-tutorial</a>; step by step <a href="demos/ab-tutorial.ps">instructions for the ab-tutorial</a>. [PostScript]</li>
</ul>
-->
<h2><a name="feedback"></a>CONTACT/FEEDBACK</h2>
<p>If you have any comments, questions, or suggestions, please let
us know by mailing "<code>doedel at cse dot concordia dot ca</code>" with "<code>Subject:
AUTO Related</code>." An enquiry should include full name and affiliation.</p>
<p class="foot">Maintained By: Pankaj Kamthan.<a href="mailto:kamthan@cs.concordia.ca"><br>
</a>(C) 1995-2010 <a href="http://cmvl.cs.concordia.ca/">Computational
Mathematics and Visualization Laboratory (CMVL)</a>. All Rights Reserved.</p>
<p class="navigation" align="center">| <a href="#announcements">Announcements</a> | <a href="#introduction">What is AUTO?</a> | <a href="#evolution">Evolution</a> | <a href="#distribution">Distribution</a> | <a href="#documentation">Documentation</a> | <a href="#applications">Applications</a> | <a href="#related_software">Related Software</a>
| <a href="#lecture_notes">Lecture Notes</a> |</p>
</body></html>