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AUTO 97

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 97 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 of AUTO is written in Fortran 77; see AUTO 2000 for the C version of AUTO and AUTO-07P for the latest Fortran 95 version with multiprocessor support.

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
  • Fortran
Platform
  • Unix
  • Linux
Availability
Free to download from the internet: http://cmvl.cs.concordia.ca/auto/
Contact Person
References to Papers
  1. E.J. Doedel, A.R. Champneys, T.F. Fairgrieve, Yu.A. Kuznetsov, B. Sandstede & X. Wang (1997)
    "AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont)" 
    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, H.B. Keller & J.P. Kernévez (1991)
    "Numerical analysis and control of bifurcation problems: (II) Bifurcation in infinite dimensions"
    Int. J. Bifurcation & Chaos 1(4): 745-772
  4. E.J. Doedel, H.B. Keller & J.P. Kernévez (1991)
    "Numerical analysis and control of bifurcation problems: (I) Bifurcation in finite dimensions"
    Int. J. Bifurcation & Chaos 1(3): 493-520
  5. 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.
  6. E.J. Doedel (1981)
    "AUTO, a program for the automatic bifurcation analysis of autonomous systems"
    Cong. Numer. 30: 265-384
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