Flow displacements in homogeneous porous media can result in instabilities at the interface between the fluids. Such instabilities may dramatically affect the overall efficiency of the displacement process and often need to be controlled. Flows that involve time-dependent injection schemes are analyzed to determine their effects on the growth of instabilities and the nonlinear development of finger structures in immiscible displacements. Predictions for monotonic and cyclic schemes in radial displacements are presented and compared with their constant injection counterpart. Moreover a controlled injection scheme that allows minimizing the instabilities is proposed. A hybrid model accounting for the discontinuities across the interface is implemented, and the problem is solved numerically. The effects of different parameters including the phase shift, amplitude, and period as well as the role of the mobility ratio and surface tension are discussed. A set of injection policies are observed to lead to the strongest attenuation of instabilities. Moreover, optimal phase shifts for cyclic displacements can result in the strongest enhancement or attenuation of the instability, depending on whether the flow involves extraction. A novel approach, referred to as the controlled injection scheme, has also been proposed and analyzed. In this scheme the flow is continuously adjusted in response to the growth rate of the instabilities resulting in a better capability of suppressing the development and growth of fingers.