Yes it can handle it I'm suggesting a shark fin curve as a good model for technical innovation.

Think about it. Take airplanes or even oil discovery the changes where slow at the beginning then exploded exponentially then hit physical limits then effectively when to zero. Cars today for example are effectively at the end of their technical advancement as far as being transportation devices. The difference between a cheap Ford and a Mercedes are pretty small. Compare this to a luxury car in the 1920 vs a pedestrian model.

Plus I thin the shark fin curve for respiration bears a lot of similarity to oil extraction and also the financial one for patent drugs. Investment in the texas oil fields for example followed a shark fin model and in general this holds for commodities. The increase exponentially till the returns become unattractive vs other investment choices then drop to zero when they are unprofitable. So both the technology and the financial model could be plausibly modeled as shark fins.

And to top it off shark fin curve has a nice ominous ring to it :)

Export land is also a shark fin in profile if you assume that no other real economic value is created. Internal consumption increases exponentially until exports no longer cause increasing revenue then the economy collapses. So I think a lot of these perturbations are better modeled as a shark fin curves first order. A eventual return to Gaussian/exponential on the back side of the curve makes them fairly physical but this is just the inherent Gaussian in effect reasserting itself. The geologic situation is inherently a gaussian so like Russian production it tends to get back on curve.

But dolphin fin curve does not have the same ring :)