We consider a network of three identical neurons with multiple signal transmission delays. The model for such a network is a system of delay differential equations. With the aid of the symbolic computation language MAPLE, we derive the corresponding system of ordinary differential equations describing the semiflow on the centre manifold. It is shown that

two cases of a single Hopf bifurcation occurs at the trivial fixed point of the full nonlinear system of delay equations, primarily as a result of the structure of the associated characteristic equation. These are (i) the simple root Hopf, and (ii) the double root Hopf. This presentation focusses on the second case, paying particular attention to possible change of criticality of the bifurcation.