  In this paper, we will perform the parameter-dependent center manifold
reduction near the generic and transcritical codimension two Bogdanov-Takens
bifurcation in classical delay differential equations (DDEs). Using a
generalization of the Lindstedt-Poincar\'e method to approximate the homoclinic
solution allows us to initialize the continuation of the homoclinic bifurcation
curves emanating from these points. The normal form transformation is derived
in the functional analytic perturbation framework for dual semigroups (sun-star
calculus) using a normalization technique based on the Fredholm alternative.
The obtained expressions give explicit formulas, which have been implemented in
the freely available bifurcation software package DDE-BifTool. The
effectiveness is demonstrated on various models.
