  We focus on the long time behavior of complex networks of reaction-diffusion
(RD) systems. We prove the existence of the global attractor and a
$L^{\infty}$-bound for a network of $n$ RD systems with $d$ variables each.
This allows us to prove the identical synchronization for general class of
networks and establish the existence of a coupling strength threshold value
that ensures such a synchronization. Then, we apply these results to some
particular networks with different structures (i.e. different topologies) and
perform numerical simulations. We found out theoretical and numerical heuristic
laws for the minimal strengh coupling needed for synchronization relatively to
the number of nodes and the network topology, and discuss the link between
spatial dimension and synchronization.
