Internal noise stochastic resonance in a cubic autocatalator

The stochastic resonance in chemical reaction systems has recently attracted growing attentions. Using chemical Langevin equation, the effect of internal noise has been studied on the dynamical behavior of a single and a one-way coupled cubic autocatalator. For the single system, it is found that the internal noise can induce sustained oscillations, and the signal-to-noise ratio (SNR) undergoes a maximum with the variation of the system size. For the coupled system, the SNR passes through a maximum with changing coupling strengths as well as with changing system sizes, which demonstrates the occurrence of the internal noise stochastic resonance (INSR) and optimal size effect. In the presence or absence of influx into the system, the coupling enhanced or suppressed INSR is found in the coupled system. All cells of the coupled system appear to exhibit INSR at an approximately equal size at a suitable coupling strength, implying that the optimal system size and coupling strength can make the system reach an optimal chemical reaction state.