Embodiments of methods of synthesizing a metathesis catalyst system, which include impregnating tungsten oxide on silica support in the presence of a precursor to produce a base catalyst; calcining the base catalyst; impregnating a metal oxide co-catalyst comprising a metal oxide onto the surface of the base catalyst to produce a doped catalyst; and calcining the doped catalyst to produce a metathesis catalyst system. Further embodiments of processes for the production of propylene, which include contacting a hydrocarbon feedstock comprising a mixture of 1-butene and 2-butene with embodiments of the metathesis catalyst system to produce, via metathesis conversion, a product stream comprising propylene.