Unfolding the fold-Hopf bifurcation in piecewise linear continuous differential systems with symmetry

► Continuous 3D symmetric piecewise linear differential systems are considered. ► One-parameter fold-Hopf bifurcation unfoldings are studied. ► The critical system exhibits a bounded set foliated by periodic orbits. ► From this set, the simultaneous bifurcation of three limit cycles is proved. ► Such fold-Hopf bifurcation is detected in a generalized version of Chua's circuit.