Hopf bifurcation in a symmetric configuration of transmission lines

We apply the equivariant degree method to a Hopf bifurcation problem for a symmetric system of neutral functional differential equations, which reflects two symmetrically coupled configurations of the lossless transmission lines. The spectral information of the linearized system is extracted and translated into a bifurcation invariant, which carries structural information of the solution set. We calculate the values of the bifurcation invariant by following the standard computational scheme and using a specially developed Maple©Maple© package. The computational results, as well as the minimal number of bifurcating branches and their least symmetries are summarized.