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AUTO 2000

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


AUTO 2000 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. Originally, AUTO was written in Fortran; see AUTO 97.

Randy Paffenroth developed a C and Python version, AUTO 2000, with lots of nice extra features, like a 3D data viewer, for example.

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
  • Maps
  • ODEs
Software Type
  • Package
  • C
  • Python
  • Unix
  • Linux
Free to download from the internet. AUTO 2000 is now on the AUTO-07P sourceforge pages.

Contact Person
References to Papers
  1. E.J. Doedel, R.C. Paffenroth, A.R. Champneys, T.F. Fairgrieve, Yu.A. Kuznetsov, B. Sandstede & X. Wang (2001)
    "AUTO 2000: Continuation and bifurcation software for ordinary differential equations (with HomCont)" (see the homepage for downloads) 
    Technical Report, California Institute of Technology.
  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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