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.
|Keywords||Bifurcation analysis, Continuation|
|References to Papers|
- 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.
- A.R. Champneys, Yu.A. Kuznetsov & B. Sandstede (1996)
"A numerical toolbox for homoclinic bifurcation analysis"
Int. J. Bifurcation & Chaos 6: 867-887.
- 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.
- E.J. Doedel (1981)
"AUTO, a program for the automatic bifurcation analysis of autonomous systems"
Cong. Numer. 30: 265-384