In the context of n-dimensional symmetric continuous piecewise linear systems with three zones and \(n\ge 2\) , the Hopf bifurcation at infinity takes place when a pair of complex conjugate eigenvalues of the linearization matrices of the external zones crosses the imaginary axis and a limit cycle of large amplitude appears. Here, we consider a degenerated situation for the same family of dynamical systems with \(n=3\) , as is the simultaneous crossing of a real eigenvalue and a complex pair along the imaginary axis. Under these conditions the bifurcation of limit cycles of large amplitude is studied, in what is known as the zero-Hopf bifurcation at infinity, following the nomenclature of smooth systems. The stability of the bifurcating limit cycle is characterized and its period and amplitude are estimated. As an application of the theoretical results, the analysis of the appearance of limit cycles of large amplitude in a Bonhöfer-van der Pol electronic oscillator due to zero-Hopf bifurcation is shown.
