  Two important classes of spatio-temporal patterns, namely, spatio-temporal
chaos and self-replicating patterns, for a representative three variable
autocatalytic reaction mechanism coupled with diffusion has been studied. The
characterization of these patterns has been carried out in terms of Lyapunov
exponents and dimension density. The results show a linear scaling as a
function of sub-system size for the Lyapunov dimension and entropy while the
Lyapunov dimension density was found to rapidly saturate. The possibility of
synchronizing the spatio-temporal dynamics by analyzing the conditional
Lyapunov exponents of sub-systems was also observed.
