Experimental results for instabilities in dump combustors have long shown the presence of some sort of hysteresis, in the vicinity of the stability boundary defined by flow speed and mixture ratio. This note reports measurements of the precise character of hysteresis loops found when the mixture ratio is Varied with flow speed held constant. The upper branch represents relatively high amplitude limit cycles and the lower branch contains low level oscillations possibly driven by stochastic sources within the chamber. Existence of the hysteresis loops suggests the possibility of causing a transition from the upper unstable branch to the lower stable branch. This has been accomplished by injecting short pulses of secondary fuel either in the boundary layer upstream of the dump plane or in the recirculation zone. Only a single pulse is required if its flow rate and width are suitably chosen. These results demonstrate the feasibility of a novel method of active control of combustion instabilities if hysteresis is present, apparently the first example of true nonlinear control of combustor dynamics. The main advantage is the small amount of secondary fuel required. More generally, this work illustrates the value, for active control, of understanding the dynamics of the uncontrolled system.