Numerical Algorithms for Nonlinear Dynamics
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Existing Program Implementations

AUTO – one of the oldest and approved packages for bifurcation analysis in the systems of ordinary differential equations (ODE), practically unsurpassed in totality of functionality, speed and reliability (see a table, comparing its capabilities with several other packages).

The first version was published in 1980, since 1986 it became AUTO86. It was written in FORTRAN and intended for operation from command line. The next version, AUTO97, have obtained GUI, rather limited.

There exist C version of the program - AUTO2000, which includes revised command line interface and possibility of controlling the program execution via PYTHON scripts.

Last-minute news (october 2006) - on the auto2000.sourceforge.net there appeared first beta-releases of the new FORTRAN version AUTO07, you may find them here ( current version)

AUTO is developed also via extensions, for example, current version includes HOMCONT (Alan Champneys, Yuri Kuznetsov, Björn Sandstede) – algorithms for the bifurcation analysis of homoclinic orbits to equilibrium points in ODEs. Separately, you may find also HomMap – the same but for maps. SlideCont (Yuri Kuznetsov ) is a driver for AUTO97, designed for bifurcation analysis of piecewise systems.

Subprograms from the AUTO package are used as bifurcation engine in many other software progects, among them I should note XPP, to which a separate song is devoted here. Freshmeat – OSCILL8, written in C#. From the most fresh – PyDSTool. It has been developed at the same university, where earlier DSTool was, it is written in PYTHON, but includes AUTO as an engine for doing bifurcation analysis.