  The existence of a global attractor for the solution semiflow of the extended
Brusselator system in the $L^2$ phase space is proved, which is a
cubic-autocatalytic and partially reversible reaction-diffusion system with
linear coupling between two compartments. The method of grouping and re-scaling
estimation is developed to deal with the challenge in proving the absorbing
property and the asymptotic compactness of this typical multi-component
reaction-diffusion systems. It is also proved that the global attractor is an
$(H, E)$ global attractor with the $L^\infty$ regularity and that the Hausdorff
dimension and the fractal dimension of the global attractor are finite. The
results and methodology can find many applications and further extensions in
complex biological and biochemical dynamical systems.
