My personal interpretation of Donnie Darko is not related to the philosophy of time travel or any of the other type of science-fiction schemes that are usually associated with the film.
Donnie is a young man who thinks constantly about girls and experiments frequently with sexual compulsions. About that matter, his parents (especially his mother, Rose) are naïve at best. Her mother is afraid and prefers Donnie attend therapy rather than confront him about his sexual growth. She pays another woman (Dr. Thurman) instead. The therapist is friendly and Donnie reveals to her some of his fantasies. It's possible that Donnie is feeling some incestuous impulses towards his sister, since he hasn't had real experience with girls.
If we flash back to the beginning of the movie, we descend upon the Carpathian Ridge, a crescent-shaped cliff that extrudes from the dense Virginia evergreens above a deep rock canyon, where a cliff marks the end of a dirt road that winds down from above. There Donnie got used to sleeping at the edge of the cliff. The close-up shows us a bike collapsed next to him, Donnie shivering, curled up in the fetal position, maybe a sign of weakness and a clue to Donnie's search for a meaning.
In the director's cut, Elizabeth asks him about Gretchen while carving a pumpkin and is curious at the Halloween party when Donnie goes upstairs with Gretchen. This may suggest Elizabeth possesses some type of control over Donnie's sexuality in the same way the mother of the family does. Donnie endures all this family control only in his subconscious, but he isn't capable of admitting it. In the first dinner scene he gets rebellious, throwing disdainful comments to his sisters and insulting his mother afterwards. His search for sexual realization is giddy, leading him to a textbook conflicted teenager scenario which creates an alternate world - in his mind - where Donnie becomes an accidental saviour while fighting against a giant bunny monster whom he calls Frank.
The bunny is the real Elizabeth's boyfriend, becoming Donnie's competitor and sexual rival. However, the external form is devoid of human attachments, only a grotesque suit, masking Donnie's guilt. All his virtual TV fantasies and fights against matriarchal repression are reflected by the artificial evil bunny, who causes him constant dreadful visions. Frank is, by this logic, a mirror of Donnie's psyche. This also would explain his rushed demeanor when he asks Gretchen to go out with him, because his desire is owerwhelmingly intense.