  In this paper, we consider the traditional Van der Pol Oscillator with a
forcing dependent on a delay in feedback. The delay is taken to be a nonlinear
function of both position and velocity which gives rise to many different types
of bifurcations. In particular, we study the Zero-Hopf bifurcation that takes
place at certain parameter values using methods of centre manifold reduction of
DDEs and normal form theory. We present numerical simulations that have been
accurately predicted by the phase portraits in the Zero-Hopf bifurcation to
confirm our numerical results and provide a physical understanding of the
oscillator with the delay in feedback.
