Perhaps you visited http://delayequations.net and were redirected. At some point in time that web address will receive its own site. For now, the following is available here:

#### Critical normal forms for delay differential equations

This is the updated version of: S.G. Janssens, *On a Normalization Technique for Codimension Two Bifurcations of Equilibria of Delay Differential Equations*, Master Thesis, Utrecht University, 2010. (**Latest update: 20 November 2018**.)

It was written under supervision of Yu.A. Kuznetsov with Odo Diekmann as co-supervisor. This updated version contains corrections and some new material – see the *Summary of updates and corrections*. As specified inside the document, it is available under a Creative Commons BY-NC-ND 4.0 International license.

#### The DelayTools package for Maple

The code that was originally part of the thesis text is being rewritten and integrated in the DelayTools package for Maple.

#### Numerical implementation in MATLAB

The newest versions of the software package DDE-BIFTOOL – maintained on SourceForge – is capable of calculating criticial normal form coefficients for local bifurcations, for the case of delay differential equations with finitely many constant delays,

\[

\dot{x}(t) = f(x(t), x(t – \tau_1),\ldots,x(t – \tau_m),\alpha)

\]

where $x(t) \in \mathbb{R}^n$, $\alpha \in \mathbb{R}^p$ is a parameter vector and $0 < \tau_1 < \ldots < \tau_m < \infty$.
This software implementation is done by Yu.A. Kuznetsov (Utrecht, The Netherlands) and M.M. Bosschaert (Hasselt, Belgium).