Stochastic bifurcation analysis in Brusselator system with white noise

Abstract

In this paper, we mainly study the stochastic stability and stochastic bifurcation of Brusselator system with multiplicative white noise. Firstly, by a polar coordinate transformation and a stochastic averaging method, the original system is transformed into an Itô averaging diffusion system. Secondly, we apply the largest Lyapunov exponent and the singular boundary theory to analyze the stochastic local and global stability. Thirdly, by means of the properties of invariant measures, the stochastic dynamical bifurcations of stochastic averaging Itô diffusion equation associated with the original system is considered. And we investigate the phenomenological bifurcation by analyzing the associated Fokker–Planck equation. We will show that, from the view point of random dynamical systems, the noise “destroys” the deterministic stability. Finally, an example is given to illustrate the effectiveness of our analyzing procedure.