The main objective of the paper is to highlight the strange and complex behaviour of a motor drive consisting of a three-phase induction machine fed by a voltage source inverter (VSI) and controlled by a hysteresis current controller (HCC). This system exhibits either periodic, subharmonic or chaotic trajectory movements, and shows bifurcation phenomena. The paper presents simulation results to introduce some astonishing properties, and applies two techniques in reaching them: continuous trajectory; and trajectory with discrete time steps. The first approach is theoretically significant while the second one represents the model of practical hardware implementation. Maps showing the chaotic and periodic regions are presented. After convincing maps regarding the chaotic nature of the system the influence of such important variables as the load torque or the speed command and parameters as the stator resistance and transient inductance is investigated. It could help either in stabilizing the periodic motions or inducing chaos. It can be concluded that periodic process cannot be maintained in wide range of change in system variables without additional measures.