  Pseudospectral approximation reduces DDE (delay differential equations) to
ODE (ordinary differential equations). Next one can use ODE tools to perform a
numerical bifurcation analysis. By way of an example we show that this yields
an efficient and reliable method to qualitatively as well as quantitatively
analyse certain DDE. To substantiate the method, we next show that the
structure of the approximating ODE is reminiscent of the structure of the
generator of translation along solutions of the DDE. Concentrating on the Hopf
bifurcation, we then exploit this similarity to reveal the connection between
DDE and ODE bifurcation coefficients and to prove the convergence of the latter
to the former when the dimension approaches infinity.
