In the design of rotating machines the clearances between the rotating and stationary parts are often made smaller in order to increase their efficiency. Although the smaller clearance provides an advantage from the performance point of view, it is however not the case when viewed from the dynamics perspective as the possibility of rotor-to-stator rub to occur increases significantly. Rubbing in rotating machines is a highly nonlinear phenomenon and therefore it is very important to understand its dynamics. In this work the bifurcations in the response of a Jeffcott rotor subjected to rotor-to-stator rub is numerically investigated. In particular the influence of the rotor imbalance, contact stiffness and friction coefficient on the response of the rotor is examined for a range of operating speed. For the range of parameters investigated in this work, numerical results revealed the occurrence of sub-synchronous, quasi-periodic and chaotic vibrations in the response of the rotor. The range of operating speed where sub-synchronous and non-synchronous vibrations were found in the rotor's response was seen to increase as a result of increasing the magnitudes of the rotor imbalance and contact stiffness. The response of the rotor was generally found to be invariant to the variation of the friction coefficient magnitude except for the combination of the largest values of rotor eccentricity and contact stiffness, whereby the range of sub-synchronous and non-synchronous vibrations was observed to increase as the magnitude of the friction coefficient became larger. For these particular magnitudes of rotor eccentricity and contact stiffness, the rotor response exhibited hysteresis phenomena resulting in the presence of multiple attractors for the same set of parameter values.