Explicit internal signal stochastic resonance in a chemical model

Abstract

A Belousov–Zhabotinsky (BZ) reaction model subject to additive Gaussian white noise is investigated as the model system is located in the dynamical region of period-1 oscillation. The model is composed of three ordinary differential equations representing the time evolutions of HBrO₂ , Ce(IV), and BrCH(COOH)₂ , respectively. Noise is separately added to the three equations. In all three cases the change in the Ce(IV) variable's output signal-to-noise ratio (SNR) as a function of the noise intensity shows non-monotonic behavior, indicating the occurrence of explicit internal signal stochastic resonance. However, its strength is quite different in each case, implying that the three reacting species play different roles in determining the dynamical behavior in the BZ reaction. The change in the peak height of the Ce(IV) variable's output frequency spectrum and the shift of the peak's central frequency with increasing noise intensity are also examined.