DDE-BIFTOOL is a collection of Matlab routines for numerical bifurcation analysis of systems of delay differential equations with discrete constant and state-dependent delays. The package supports the following functionality:

• computation, continuation and stability analysis of steady state solutions and periodic solutions,
• continuation of Hopf and fold bifurcations of equilibria
• continuation of folds, period doublings and torus bifurcations of periodic orbits (new from version 3.0)
• computation of normal form coefficients for Hopf, double-Hopf and zero-Hopf bifurcation (constant delays only, new from version 3.1)
• continuation of connecting orbits (constant delays only)
• continuation of relative equilibria and relative periodic orbits in systems with rotational symmetry (constant delays only, new from version 3.0).

The figure shows a typical result that can be achieved using DDE-BIFTOOL. The two-parameter bifurcation diagram was obtained for the Duffing oscillator with delayed feedback, as discussed in the large-delay limit by Yanchuk & Perlikowski in (PRE79, 0462211, 2009). The parameters were the delay (tau) and the feedback gain (b). 

For a quick tour of DDE-BIFTOOL's capabilities have a look at the online demos at ddebiftool.sourceforge.net/demos/index.html.

Compatibility: Matlab version 7 or later, Octave version 3.2 or later.

Manual on arxiv: arxiv.org/abs/1406.7144, see also tutorial demos at download page.