The existence of a compact uniform attractor for a family of processes corresponding to the dissipative non-autonomous Klein-Gordon-Schrödinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.

We considered the longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon-Schrödinger equation (KGS lattice system). We first proved the existence of a global attractor for the system considered here by introducing an equivalent norm and using "End Tails" of solutions. Then we estimated the upper bound of the Kolmogorov delta-entropy of the global attractor by applying element decomposition and the covering property of a polyhedron by balls of radii delta in the finite dimensional space. Finally, we presented an approximation to the global attractor by the global attractors of finite-dimensional ordinary differential systems.