Of course, there is; it should be not too difficult to look for articles by key words; definitely this is not a simple, but a complex question because the cultural background of gender relations and the actual relations between father(s) and mother(s) in a family are to consider; this is a very dynamic relation in western families where the roles of parents are don't mean a subordination of the female part of parents under the male part, but equal rights (with different roles in everyday life) play a role. Also the concept of "authoritarian" has changed in modernity.

I repeat, there is a gender difference

Although there is a complex relationships in this direction as Dr Hein Retter has explained, in our developing countries this difference may be disappeared. This may be related to the social community where the mother takes the role of father and vise versa. In this case one of them acts as both for different abnormal life. The reasons many and cannot be accounted simply.