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AUTO-07P

AUTO is a software package for continuation and bifurcation problems in ODEs. The package includes HomCont, algorithms for the bifurcation analysis of homoclinic orbits.

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AUTO-07P is a publicly available software for continuation and bifurcation problems in ordinary differential equations originally written in 1980 and widely used in the dynamical systems community. This version is written in Fortran 95. See also AUTO 97 and AUTO 2000 for older versions. AUTO-07P succeeds both.

A completely new three-dimensional plotting utility, PLAUT04, is included. 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 also contains the package HomCont which was developed by Alan Champneys, Yuri Kuznetsov and Björn Sandstede. HomCont is a toolbox for numerical homoclinic bifurcation analysis. It deals with continuation of codimension-1 homoclinic orbits to hyperbolic and saddle-node equilibria, including the detection of many codimension-2 singularities and the continuation of these singularities in 3 or more parameters.

KeywordsBifurcation analysis, Continuation
Model
  • Maps
  • ODEs
Software Type
  • Package
Language
  • C
  • Fortran
  • Python
Platform
  • Unix
  • Linux
  • Windows
  • MacOS
Availability

Free to download from the internet (BSD-style license): http://cmvl.cs.concordia.ca/auto/

Contact Person
References to Papers
  1. E.J. Doedel (2007) "AUTO-07P: Continuation and bifurcation software for ordinary differential equations" (see the homepage for downloads) Technical Report, Concordia University.
  2. A.R. Champneys, Yu.A. Kuznetsov & B. Sandstede (1996) "A numerical toolbox for homoclinic bifurcation analysis" Int. J. Bifurcation & Chaos 6: 867-887.
  3. E.J. Doedel & J.P. Kernévez (1986) "AUTO: Software for continuation problems in ordinary differential equations with applications" Technical report, Applied Mathematics, California Institute of Technology.
  4. E.J. Doedel (1981) "AUTO, a program for the automatic bifurcation analysis of autonomous systems" Cong. Numer. 30: 265-384
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