Consider the scalar differential-delay equation
with , , , , – and are bifurcation parameters. (1) exhibits codimension-one and codimension-two bifurcations. For , , a codimension-three bifurcation occurs, i.e., triple-zero bifurcation. Using center manifold theory, the authors derive the following normal form with universal unfolding
They determine the bifurcations occurring in the truncated normal form, namely transcritical, Hopf, Takens-Bogdanov, zero-Hopf ones. Finally, numerical simulations are presented.