A Hopf-Zero Degenerated Case in Symmetric Piecewise Linear Systems

A possible degeneration of the Hopf-zero bifurcation for symmetric three-dimensional piecewise linear differential systems with three zones is studied in a two-parameter plane. We show that around the critical point in such parameter plane the unfolding is very similar to the one appearing in the generalized Hopf bifurcation of differentiable dynamics.