In this paper the quasilinear second order parabolic systems of reaction-diffusion type in an unbounded domain are considered. Our aim in this article is to study the long-time behaviour of parabolic systems for which the nonlinearity depends explicitely on the gradient of the unknown functions. To this end we give a systematic study of given parabolic systems and their attractors in weighted Sobolev spaces. Dependence of the Hausdorff dimension of attractors from weight of the Sobolev spaces are considered
