Approximation of Attractors of Nonautonomous Lattice Dynamical Systems

The aim of this paper is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form $u_i^{\mathrm{\prime }}=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_i+F(u_i)+f_i(t)(i\in \mathbb{Z})(\ast )$. We show that the finite-dimensional approximations for (*) are uniformly dissipative. The upper semi-continuous convergence of the attractors of the finite-dimensional approximations is established.