Donnie Darko is a perfect example of chaos. It's a movie about a schizophrenic boy (Donnie Darko) who is awakend by a man in a bunny rabbit suit on October 2nd 1988 (Frank) and he tells him the world will end in 28 days. When he is told by Frank to come with him in the night a jet engine falls into his room, sparing his life. I recommend you watch it.
"Some viewers theorize, at midnight on October 2, a "Tangent Universe" branches off the "Primary Universe" around the time when Donnie is called out of his bedroom by Frank, immediately before the appearance of the Artifact, the faulty jet engine. The inherently unstable Tangent Universe will collapse in just over 28 days and take the Primary Universe with it if not corrected. Closing the Tangent Universe is the duty of the "Living Receiver", Donnie, who wields certain supernatural powers to help him in the task.
Those who die within the Tangent Universe and would not have died otherwise are the "Manipulated Dead" (Frank, Gretchen). Frank, at least, is also given certain powers in that he is able to subtly understand what is happening and to contact and influence the Living Receiver via the "Fourth Dimensional Construct", water. All others within the orbit of the Living Receiver are the "Manipulated Living" (e.g. Ms. Pomeroy, Dr. Monnitoff), subconsciously drawn to push him towards his destiny to close the Tangent Universe and, according to the Philosophy of Time Travel, die by the Artifact.
Frank appears in the story in two guises (three guises if we assume that he "never" dies on account of the restoration of the Primary Universe through the negation of the Tangent Universe). First, there is the Manipulated Dead Frank who appears to Donnie as a premonition from the future of the Tangent Universe in the disturbing rabbit suit. Dead Frank is aware of Donnie's fate and destiny, and impels him to realize it so that the Primary Universe can be restored at the point where/when the Tangent Universe branched off from it. Second, Frank appears alive as Donnie's sister's boyfriend, whose fate unfolds within the Tangent Universe by means of Donnie's successes in realizing his mission. This living boyfriend is fatally shot by Donnie towards the end of the film, a killing which was foreseen by Donnie." - Wikipedia
So the death of Donnie creates a major disturbance in the future, essentially saving the Universe.