Chains of model structures arising from modules of finite Gorenstein dimension

For any integer n 0 and any ring R, \ (PGFₙ, \ Pₙ^ PGF^) proves to be a complete hereditary cotorsion pair in R-Mod, where PGF is the class of PGF modules, introduced by J. Saroch and J. S\'tov\'icek, and \ PGFₙ is the class of R-modules of PGF dimension n. For any Artin algebra R, \ (GPₙ, \ Pₙ^ GP^) proves to be a complete and hereditary cotorsion pair in R-Mod, where GPₙ is the class of modules of Gorenstein projective dimension n. These cotorsion pairs induce two chains of hereditary Hovey triples \ (PGFₙ, \ Pₙ^, \ PGF^) and \ (GPₙ, \ Pₙ^, \ GP^), and the corresponding homotopy categories in the same chain are the same. It is observed that some complete cotorsion pairs in R-Mod can induce complete cotorsion pairs in some special extension closed subcategories of R-Mod. Then corresponding results in exact categories PGFₙ, \ GPₙ, \ GFₙ, \ PGF^<, \ GP^< and GF^<, are also obtained. As a byproduct, PGF = GP for a ring R if and only if PGF^ₙ= Pₙ for some n.