Modeling of Nonlinear Chemical Reaction Systems and Two-Parameter Stochastic Resonance

The idea of stochastic resonance (SR) is extended to two-parameter dynamical systems based on the Oregonator model of the Belousov-Zhabotinsky (BZ) reaction. The first case presents the photosensitivity of the reaction, and light flux and a flow rate are the two control parameters. The second case presents the effect of temperature on the oscillatory behaviors, and temperature and a flow rate are the control parameters. Stochastic resonance is demonstrated in the first case in which a signal and noise are applied to the different inputs, respectively. The scenario and novel aspects of SR in two-parameter systems are discussed, and the possibility of the analogous SR in biological systems is also pointed out.

Fig. 1. Two different directions of a Hopf bifurcation of a photosensitive chemical oscillator: (a) Subcritical Hopf bifurcation, (b) Supercritical Hopf bifurcation.