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

Nonresonant Hopf-Hopf bifurcation and a chaotic attractor in neutral functional differential equations