We present experimental and theoretical investigations of the nonlinear resonance behavior of a focal steady state in the Belousov-Zhabotinsky (BZ) reaction which is perturbed by its own dynamics. For this purpose the outputs of two independent BZ-oscillators of incommensurate frequencies are linearly combined in analogy to a simple feed-forward net to achieve the quasiperiodic driving of a third BZ-reactor which is in a focal steady state. For low amplitudes of the quasiperiodic flow-rate perturbations the response is also quasiperiodic in the focal BZ-reactor. Above a threshold value of the quasiperiodic amplitudes, however, single bursts are observed at small phase differences between the two perturbing oscillators. A further increase in the amplitude leads to groups of bursts with small oscillations in between. Aperiodic stochastic bursting in the BZ-reactor is observed when the flow-rate into the focal reactor is perturbed by Gaussian distributed white noise of sufficiently high amplitude and pulse length. The experiments are shown to agree with computer simulations using the Showalter-Noyes-Bar-Eli (SNB) model. At high amplitudes of quasiperiodic forcing the SNB-model gives evidence for the existence of an attractor which is strange but nonchaotic (information dimension = 2.0).