In a dynamic simulation method recently developed for accelerator-driven subcritical waste transmutation systems, power levels are renormalized dynamically based on the changing reactivity of the flowing system. For such systems, the power varies directly with the source strength, and inversely with the reactivity. The prompt-jump form of the point-kinetics equations has been used to provide the dynamic renormalization factor for the spatially dependent flowing-fuel system. A unique characteristic of the source-dominated system has been discovered. In the traditional reactor system, power changes are controlled by the half-life for decay of the longest-lived delayed neutron precursors. For the source-dominated system, the delayed neutron precursors do not appreciably slow the response of the system.