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Normal curves are symmetrical, but Lotka-Volterra (predator-prey) cycles are skewed to the left (crash is faster than growth). It depends on what assumptions you put into the model.
You can include a "effort function" in the D.E. that approximates how the market responds to scarcity. If the effort function is linear($X increase in price of oil always results in $Y increase in investment), there is no change to the shape of the resulting curve; it is still a normal curve, just a bit taller and shifted to the right.
To change the shape will require an "unreasonably aggressive surge in investment".
My technology effect concept is exactly a predator prey relationship. In this case the predator is advancing technology. And the prey is a poor little oil drop. Advancing technology is what transforms a symmetric relationship into a asymmetric one. Noye Moore's law effectively has this form. Eventually it reaches a real physical limit and transistor size no longer shrinks. In my opinion just about every example of refining technology to increase some variable results in a predator prey like relationship.
Thanks for real name for the curve I've been using shark fin.
Still like shark fin though :)