Periodicity suppression and period-adding caused by a parametric excitation in the Lorenz system

In this paper, we propose a continuous-time nonautonomous three-dimensional dynamical system, which was obtained from the original Lorenz system by introducing a parametric sinusoidal excitation. We show that, depending on the magnitude of the angular frequency of the sinusoidal excitation, two independent phenomena may occur: (i) the complete suppression of the periodic structures embedded in the chaotic region of the $$(r,\sigma )$$ parameter plane of the original Lorenz system, resulting in a chaos region completely free from periodic windows, and (ii) the appearance of other periodic structures, this time organized in period-adding sequences, embedded in the chaotic region of this same parameter plane