AUTO
SOFTWARE FOR CONTINUATION AND BIFURCATION PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

This is the Home Page of the AUTO Web Site, established in January 1996.

ANNOUNCEMENTS

INTRODUCTION

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.

AUTO can do a limited bifurcation analysis of algebraic systems of the form

f(u,p) = 0,    f,u in Rn

and of systems of ordinary differential equations of the form

u'(t) = f(u(t),p),    f,u in Rn

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.

For further information and details, see the AUTO Documentation.

AUTO STATUS/EVOLUTION

The following table represents the historical evolution in the development of AUTO in a chronological order.

Year Version Specification Affiliation
1976 Early program for BVP in ODEs California Institute of Technology, Pasadena, USA
1980 First distributed version Concordia University, Montreal, Canada
1986 AUTO86 California Institute of Technology, Pasadena, USA
1994 X/Motif version : AUTO94 California Institute of Technology, Pasadena, USA
1994 Parallel version: AUTO94P California Institute of Technology, Pasadena, USA
1997 AUTO97, with HOMCONT Concordia University, Montreal, Canada
2000 C Language Version California Institute of Technology, Pasadena, USA
2007 AUTO-07p Concordia University, Montreal, Canada

AUTO AVAILABILITY/DISTRIBUTION

The AUTO package is available for UNIX/Linux-based computers.

AUTO-07P

AUTO-07p is the successor to both AUTO97 and AUTO2000.

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.

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 GNU Fortran 95 compiler (gfortran). Gfortran ships with most current Linux distributions.

AUTO DOCUMENTATION

The AUTO distribution include a copy of the AUTO Manual in LATEX, PostScript, and Portable Document Format (PDF).

AUTO APPLICATIONS

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".

RELATED SOFTWARE

Other software directly or indirectly related to AUTO includes DSTool, PyDSTool, XPPAUT, Content, MatCont, and DDE-BifTool.

RELATED LECTURE NOTES

CONTACT/FEEDBACK

If you have any comments, questions, or suggestions, please let us know by mailing "doedel at cse dot concordia dot ca" with "Subject: AUTO Related." An enquiry should include full name and affiliation.

Maintained By: Pankaj Kamthan.
(C) 1995-2010 Computational Mathematics and Visualization Laboratory (CMVL). All Rights Reserved.