Summary: We analyze a modified van der Pol-Duffing electronic circuit, modeled by a three-dimensional autonomous system of differential equations with \(\mathbb{Z}_2\)-symmetry. Linear codimension-one and -two bifurcations of equilibria give rise to several dynamical behaviours, including periodic, homoclinic and heteroclinic orbits. The local analysis provides, in first approximation, different bifurcation sets. These local results are used as a guide to apply the adequate numerical methods to obtain a global understanding of the bifurcation sets. The study of normal form of the Hopf bifurcation shows the presence of cusps of saddle-node bifurcations of periodic orbits. The existence of a codimension-four Hopf bifurcation is pointed out. In the case of the Takens-Bogdanov bifurcation, we analyze several degenerate situations of codimension-three in both homoclinic and heteroclinic cases. We also show the existence of a Hopf-Shil’nikov singularity.