[WEIZMANN_LOGO] Faculty of Mathematics and Computer Science
Weizmann Institute of Science

Dynamical Systems Software:
I describe here only packages distributed freely*, for numerical analysis of dynamical systems. This include computing trajectories, phase-space and bifurcation diagrams.

Disclaimer: I only indicate some capabilities, and I am not an expert in any of them, and I am working only on ODE at the current time.

AUTO: This is a continuation package, namely, package to perform bifurcation analysis of FPs and limit cycles as well as computation of some solutions of parabolic PDEs. Notice that there is an option to do "time-evolution" integration in order to find FPs.

XPPAUT: It includes GUI and use AUTO for bifurcation analysis. It is also capable of solving differential equations.

I found the appendix on XPPAUT in the book: "Computational Cell Biology", by Fall, Marland, Wagner and Tyson, (Editors) Springer-Verlag 2002, to be very good for a novice.
The above is the XPP tutorial (chapter 2) from Brad Ementrount's book on XPP.

MATCONT: Continuation package for Matlab (*while the package is free, Matlab is not, but they are usually available in universities at least here).


Simple AUTO examples

General comment for beginners: in all the packages you need to scale your equations, so the dynamical range of each of the variables is centered around 1. That is, the variables and parameters should be in the range of let say [10^-3,10^3], so you'll get a reasonable accuracy in a reasonable time.

On the availability of these SWs for Weizmann users:

AUTO/07p is installed on the math13-lx Linux machine, without the GUI or the 3D plotting utility (2D plotting tool is working). You can use Matlab for the visualization, you can contact me for a matlab code that process auto's output files. The complete installation on Ubuntu is possible after a careful reading of the relevant three pages in the manual, even by someone who has no experience in Linux installation (i.e. me).

You can use the XPP for windows on any PC without installation, if you have the Exceed (which are installed on most PCs) open as your X-windows terminal.
Notice: when working with the Exceed X-windows environment, if are logging form e.g., home, to your office computer, the Exceed needs to restart the display. This will end up in crashing all your x-application, so beware.