I added to the boring stub a discussion of how it can be chaotic.
So far I've developed the discrete case.
The continuous case displays chaos if the logistic growth model is given delayed feedback.
As for how the logistic function describes oil depletion, see [The Derivation of "Logistic-shaped" Discovery](http://www.theoildrum.com/node/4171) in The Oil Drum. The point is that the logistic function describes discovery. The rate of discovery of new oil fields grows with the rate of search and decreases with the fraction of fields left to discover.