  Through numerical simulations we analyze the synchronization time and the
Lyapunov dimension of a coupled map lattice consisting of a chain of chaotic
logistic maps exhibiting power law interactions. From the observed behaviors we
find a lower bound for the size $N$ of the lattice, independent of the range
and strength of the interaction, which imposes a practical lower bound in
numerical simulations for the system to be considered in the thermodynamic
limit. We also observe the existence of a strong correlation between the
averaged synchronization time and the Lyapunov dimension. This is an
interesting result because it allows an analytical estimation of the
synchronization time, which otherwise requires numerical simulations.
