The 4.5 minutes guide to AUTO

Experienced users of AUTO most probably know about an interesting phenomenon. It takes less that five minutes to explain AUTO to novice users, while it seems almost impossible to start with the manual. The intention of this section is to provide more or less this `less than five minutes' introduction.

If you are familiar with AUTO you may skip this section and start reading with Section `Running rauto' on page . The following description of AUTO will be on the version AUTO97. There has been a number of changes in AUTO2000, but we stick to AUTO97 here, because the basic principle of use did not change and AUTO97 still seems to be a quite popular version. Rauto should work as well with AUTO2000. A new version AUTO07 is under development and we will upgrade rauto and this description sometimes after it became the new official version (more precisely, after the author decides to switch to AUTO07).

AUTO is a software package for computational bifurcation analysis of generic dynamical systems. The most commonly used features are the computation of families of equilibrium points and periodic solutions of autonomous ODEs

$$\dot{x} = f(x,\mu), \qquad x\in\mathbb{R}^n,\quad \mu\in\mathbb{R}^m$$ (B.1)

and their local bifurcations, and in this tutorial we will focus on problems of this type. AUTO offers substantially more functionality, but the principal of use remains always the same. Please see the reference manual [1] for more information.

The first you need to know is that AUTO is neither a stand-alone program nor a library, it is something in between. AUTO is an almost complete program that comes as a library. It is incomplete because it naturally lacks the subroutines defining your right-hand-side of ODE (1) and it has the form of a library because that's the easiest way to deal with this situation. However, you don't need to worry too much about these things, because rauto takes care of the messy part. It is just a little helpful to know that running rauto involves compiling and linking of Fortran files and that you might be confronted with error messages from the Fortran compiler. But we are running ahead, let's start at the beginning.