Turing Instability and Hopf Bifurcation for the General Brusselator System
The Brusselator system subject to homogeneous Neumann boundary conditions is investigated. It is firstly shown that the homogeneous equilibrium solution becomes Turing unstable or diffusively unstable when parameters are chosen properly. Then the existence of Hopf bifurcation to the ODE and PDE models is obtained. Examples of numerical simulations are also shown to support and supplement the analytical results.
G. H. Guo and B. F. Li, "Turing Instability and Hopf Bifurcation for the General Brusselator System", Advanced Materials Research, Vols. 255-260, pp. 2126-2130, 2011