Attractors for one kind of lattice dynamical system

In the present paper, we study the asymptotic behavior of the solutions for one kind of lattice dynamical system. The existence theorem for the global attractor in l2×l2l2×l2 is established by using a recent result [Q.F. Ma, S.H. Wang, C.K. Zhong, Necessary and sufficient conditions for the existence of global attractors for semigroups and applications, Indiana Univ. Math. J. 51 (2002) 1541–1559] instead of applying the asymptotic compactness condition. And the upper semicontinuity of the global attractor is also proved.