The stochastic Hopf bifurcation analysis in Brusselator system with random parameter

Abstract

Hopf bifurcation in Brusselator system with random parameter is explored in this paper. Firstly according to the orthogonal polynomial approximation in Hilbert space, the Brusselator system with random parameter can be reduced into the deterministic equivalent system. Then the Hopf bifurcation in deterministic equivalent system is discussed by the mathematical analysis and the first Lyapunov coefficient method. The studies discovered that different from the deterministic system, the critical value of stochastic Hopf bifurcation is determined not only by deterministic parameters in stochastic system, but also by the intensity of random parameter. As the intensity of random parameter is increased, the critical value of stochastic Hopf bifurcation is decreased. At last theoretical results are verified by numerical simulations.