A human hair sheitel is hair that was already detached from the natural source (a person’s head) therefore the concern of gozez because of brushing does not apply. The same halacha applies to a non-human hair sheitel. Therefore, you are allowed to use a brush with hard bristles.However, one should still use a different brush than the one used during the week(Toras Hamelochos page 179).The Minchas Shabbos (80:117)says that one can be lenient and permit brushing (even vigorously) a synthetic sheitel but not for a human hair.The Shemiras Shabbos K’hilchoso (14:46) says one should brush a sheitel with the same Halachos as regular hair on shabbos.Aside from the issur of gozez one should not brush one’s sheitel because doing so would be tikun munei if the sheitel would not be worn without brushing(Ketzos Ha’shulchan 143:badi 6, Klalim ibid:page 541).
Summary of:
http://www.thehalacha.com/attach/Volume3/Issue11.pdf