Global dissipative dynamics of the extended Brusselator system

The existence of a global attractor for the solution semiflow of the extended Brusselator system in the L2L2 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 rescaling estimation is developed to deal with the challenge in proving the absorbing property and the asymptotic compactness of this typical multi-component reaction–diffusion system. The regularity and the finite dimensionality of the global attractor are also studied. The results and methodology can find many applications and further extensions in investigations of complex biological and biochemical dynamical systems.