Hopf bifurcations in general systems of Brusselator type

This paper is concerned with general models of Brusselator type subject to the homogeneous Neumann boundary condition. The existence of Hopf bifurcation for the ODE and PDE models is obtained. By the center manifold theory and the normal form method, the bifurcation direction and stability of bifurcating periodic solutions are established. Moreover, some numerical simulations are shown to support the analytical results.