  Nonresonant Hopf-Hopf singularity in neutral functional differential equation
(NFDE) is considered. An algorithm for calculating the third-order normal form
is established by using the formal adjoint theory, center manifold theorem and
the traditional normal form method for RFDE. Van der Pol's equation with
extended delay feedback is studied as an example. The unfoldings near the
Hopf-Hopf bifurcation point is given by applying this algorithm. Periodic
solutions, quasi-periodic solutions are found via theoretical bifurcation
diagram and numerical illustrations. The Hopf-Hopf bifurcation diagram
indicates the possible existence of a chaotic attractor, which is confirmed by
a sequence of simulations.
