Hopf bifurcation in a reaction-diffusion system with conservation of mass

Hopf bifurcation in a mass conserved reaction-diffusion system is studied by applying the method of local bifurcation analysis. The normal form in the presence of 0 : 1 mode interaction on the centre-stable manifold is derived from the reaction-diffusion system. It is observed that the normal form has Hopf instability points around non-trivial equilibria. In this situation, the normal form can be renormalized into the normal form for the Hopf bifurcation. As a result, the local stabilities of small amplitude time-periodic solutions of the original reaction-diffusion system can be determined by using the normal form.