  We study traveling wave solutions of the Kerner--Konh\"auser PDE for traffic
flow. By a standard change of variables, the problem is reduced to a dynamical
system in the plane with three parameters. In a previous paper (Carrillo, F.A.,
J. Delgado, P. Saavedra, R.M. Velasco and F. Verduzco, (2013). Traveling waves,
catastrophes and bifurcations in a generic second order traffic flow model --to
appear in \textit{International Journal of Bifurcation and Chaos}--, it was
shown that under general hypotheses on the fundamental diagram, the dynamical
system has a surface of critical points showing either a fold or cusp
catastrophe when projected under a two dimensional plane of parameters named
$q_g$--$v_g$. In any case a one parameter family of Bogdanov--Takens (BT)
bifurcation takes place, and therefore local families of Hopf and homoclinic
bifurcation arising from each BT point exist. Here we prove the existence of a
degenerate Bogdanov--Takens bifurcation (DBT) which in turn implies the
existence of Generalized Hopf or Bautin bifurcations (GH). We describe
numerically the global lines of bifurcations continued from the local ones,
inside a cuspidal region of the parameter space. In particular, we compute the
first Lyapunov exponent, and compare with the GH bifurcation curve. We present
some families of stable limit cycles which are taken as initial conditions in
the PDE leading to stable traveling waves.
