The effect of hyperesthesia of characteristics of vibrations while adding the table salt (NaCl) as a trace substance into the reaction medium has been found for the Briggs–Rauscher oscillating reaction. The cycle of oscillations has already changed when the concentration of NaCl was 0.006 % of the total volume of the mixture. The so-called threshold effect involving the shutoff of self-induced vibration regime during one of the phases (dark or light phase) according to the concentration of NaCl was discovered. With the introduction of ethanol or acetone the significant change in the reaction has occurred at minimal concentration: 0.8 % for ethanol, 1.7 % for acetone. Different concentration of the trace substance leads to the change of the time and number of oscillations and the total time of self-induced vibration regime, the amplitude, and the form of relaxation vibrations of electrochemical potential. The conclusion about the degree of control of the process of oscillations and its shutoff in the certain phase by adding the trace substances into the reactions has been made. The quantitative basis for identifying of described and other substances (and their weak external influences) is meant to be the correlation between the oscillation frequency (period) and the concentration of the reagent and the catalyst. The information, described in the work for chemical oscillator, is confirmed by biological self-oscillating processes. The threshold effect, found in the work, may be useful for understanding of the specifics of the fading stage in biological oscillators.