  In this work the existence and properties of a global attractor for the
solution semiflow of the Oregonator system are proved. The Oregonator system is
the mathematical model of the famous Belousov-Zhabotinskii reaction. A
rescaling and grouping estimation method is developed to show the absorbing
property and the asymptotic compactness of the solution trajectories of this
three-variable reaction-diffusion system with quadratic nonlinearity from the
autocatalytic kinetics. It is proved that the fractal dimension of the global
attractor is finite. The existence of an exponential attractor for this
Oregonator semiflow is also shown.
