Resonance Analyses for a Noisy Coupled Brusselator Model

We discuss the dynamical behavior of a chemical network arising from the coupling of two Brusselators established by the relationship between products and substrates. Our interest is to investigate the coherence resonance (CR) phenomena caused by noise for a coupled Brusselator model in the vicinity of the Hopf bifurcation, which can be determined by the signal-to-noise ratio (SNR). The CR in two coupled Brusselators will be considered in the presence of the Gaussian colored noise and two uncorrelated Gaussian white noises. Simulation results show that, for the case of single noise, the SNR characterizing the degree of temporal regularity of coupled model reaches a maximum value at some optimal noise levels, and the noise intensity can enhance the CR phenomena of both subsystems with a similar trend but in different resonance degrees. Meanwhile, effects of noise intensities on CR of the second subsystem are opposite for the systems under two uncorrelated Gaussian white noises. Moreover, we find that CR might be a general phenomenon in coupled systems.