Effects of combined harmonic and random excitations on a Brusselator model

We discuss the constructive role of combined harmonic and random excitation on stochastic resonance (SR) in a Brusselator model. We first numerically investigate SR determined by the Signal-to-Noise Ratio (SNR) in this model. Effects of different parameters on SR are described in detail. Our simulation results show that the intensity of the Gaussian colored noise and the amplitude of the periodic force can enhance SR. Moreover, an analytical framework is presented for the SNR of the Brusselator model, leading to a theoretical expression of SNR. We observe a good agreement between the theoretical and numerical results, and the effectiveness of the proposed theoretical method is verified. This theoretical analysis provides a global view on how the dynamics of a periodically forced system with noise changes in the vicinity of a Hopf bifurcation.