Good.
I'm glad somebody finally tackled this.
Up till now it seems that the only possibly paradigm has been an algae boom and subsequent bust as a model for peak oil.

The top post graph is one of many possible models. It would be interesting to see some of the others too.

By merely tweaking the values of α, β, γ and δ you can get an entirely new and different model:


Note that the choice of predator and prey species are merely convenient names to assign the axes of these plots. Given appropriate parameters for Lotka-Volterra, you could just as easily be talking about SUVs and gasoline supply.