Dynamical Behavior of Brusselator System Driven by Non-Gaussian Noise

  • Qiang Dong Tiangong University School of Mathematical Sciences, No.399 Binshui West Road Xiqing District, Tianjin300387, China
  • Yongfeng Guo Tiangong University School of Mathematical Sciences, No.399 Binshui West Road Xiqing District, Tianjin300387, China
Keywords: Non-Gaussian noise, Brusselator model, Mean first passage time, Noise enhanced stability


The non-Gaussian noise induced the mean first passage time (MFPT) in Brusselator system are examined. In this paper, the path integral method is used to approximate non-Gaussian noise to Gaussian color noise. The FPT of the 50000 response tracks is obtained by solving the system equation through the fourth-order stochastic Runge-Kutta algorithm. Then we get the MFPT. The influences of the noise intensity, correlation time and non-Gaussian parameter of non-Gaussian noise on the MFPT are characterized. We also found the noise enhanced stability (NES) phenomenon in the system.


. Gammaitoni L, Marchesoni F, Menichella-Saetta E, et al. “Stochastic resonance in bistable systems.”Physical Review Letters,vol.62,pp. 349-352,1989.

. Bag B C, Hu C K. “Escape through an unstable limit cycle driven by multiplicative colored non-Gaussian and additive white Gaussian noises.”Physical Review E,vol.75,pp. 042101,2007.

. Bag B C, Petrosyan K G, Hu C K. “Influence of noise on the synchronization of the stochastic Kuramoto model.”Physical Review E,vol.76,pp. 056210,2007.

. Shi P M, Xia H F, Han D Y, et al. “Dynamical complexity and stochastic resonance in an asymmetry bistable system with time delay.”Chinese Journal of Physics,vol.55,pp. 133-141,2017.

. Devoret M H, Martinis J M, Esteve D, et al. “Resonant Activation from the Zero-Voltage State of a Current-Biased Josephson Junction.”Physical Review Letters,vol.53,pp. 1260-1263,1984.

. Mantegna R N, Spagnolo B. “Noise Enhanced Stability in an Unstable System.”Physical Review Letters,vol.76,pp. 563-566,1996.

. Breen J, Kirkland S. “Minimising the largest mean first passage time of a Markov chain: The influence of directed graphs.”Linear Algebra and its Applications,vol.520,pp. 306-334,2017.

. Fiasconaro A, Mazo J J, Spagnolo B. “Noise-induced enhancement of stability in a metastable system with damping.”Physical Review E,vol.82,pp. 041120,2010.

. Deng X , Zheng S , Xu P , et al. “Study on dissipative structure of China’s building energy service industry system based on brusselator model.”Journal of Cleaner Production,vol.150,pp. 112-122,2017.

. Li B, Jin Y F. “The mean first-passage time for piecewise nonlinear system driven by colored correlated additive and multiplicative colored noises.”Acta Physica Sinica,vol.62,pp. 150503,2013.

. Prigogine I, Lefever R. “Symmetry Breaking Instabilities in Dissipative Systems. II.”The Journal of Chemical Physics,vol.48,pp. 1695–1700,1968.

. Zhang R T, Hou Z H, Xin H W. “Effects of non-Gaussian noise near supercritical Hopf bifurcation.” Physica A: statistical mechanics and its applications, vol.390,pp. 147-153,2011.

. BOUZAT S, WIO H S. “Current and efficiency enhancement in Brownian motors driven by non-Gaussian noises.”The European physical journal B, vol.41,pp. 97-105,2004.

. BOUZAT S, WIO H S. “New aspects on current enhancement in Brownian motors driven by non-Gaussian noises.”Physica A: statistical mechanics and its applications, vol. 351,pp. 69-78,2005.