Eur. Phys. J. B (2017) 90: 194
https://doi.org/10.1140/epjb/e2017-80076-9

Regular Article

Effects of combined harmonic and random excitations on a Brusselator model

¹ Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R. China
² School of Marine Sciences, Northwestern Polytechnical University, Xi’an 710072, P.R. China
³ Potsdam Institute for Climate Impact Research, Potsdam 14412, Germany
⁴ Department of Physics, Humboldt University Berlin, Berlin 12489, Germany
⁵ Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod 603950, Russia

^a e-mail: hsux3@nwpu.edu.cn

Received: 3 February 2017
Received in final form: 26 May 2017
Published online: 16 October 2017

Abstract

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.