Influence of diffusion on the stability of a full Brusselator model

The classic Brusselator model consists of four reactions involving six components A, B, D, E, X, Y. In a typical run, the final products $D$ and $E$ are removed instantly, while, the concentrations of the reactants A and B are kept constant. Then, the classic Brusselator model consisting of two equations for the intermediate X and Y is obtained. When the component B is not considered constant, it is added to the mixture and the so-called full Brusselator model is considered. In this paper, the full Brusselator model is studied. In particular, the boundedness of solutions and the effect of diffusion on the linear stability is analyzed. Moreover, sufficient conditions ensuring that the unique steady state, unstable (stable) in the ODEs system, becomes stable (unstable) in presence of diffusion, are performed and a first nonlinear stability result is obtained.