I found some of the explanation of the cobweb model from Wikipedia helpful.

Simplifying, the cobweb model can have two main types of outcomes:

(1)If the slope of the supply curve is greater than the slope of the demand curve (in absolute value), then the fluctuations decrease in magnitude with each cycle, so a plot of the prices and quantities over time would look like an inward spiral, as shown in the diagram. This is called the stable or convergent case.

(2) If the slope of the supply curve is less than the slope of the demand curve (in absolute value), then the fluctuations increase in magnitude with each cycle, so that prices and quantities spiral outwards. This is called the unstable or divergent case.

Oil prices would seem to be the divergent case.

It seems to me though that the world's economy is in a sufficiently weak state that the very first bounce up will cause massive bankruptcies, and possible collapse of financial systems around the world. I am not sure that we will have to wait for multiple iterations to happen.

I agree that, depending on the resiliency of the global economy, we may not sustain very many wild swings in the dollar-price of oil. I do, however, think that we need to also measure volatility in the ratio of $/barrel:$/year median income.

In theory, oil could hold steady at exactly $40/barrel, but this could represent massive price volatility if there are wild swings in household income, inflation leading to deflation or vice-versa, etc...

As useful as it is for a snapshot, IMO the Cobweb Model cannot account for the system dynamics. Take a look at almost any real-world system's time history and you'll see the same quasiperiodic but unpredictable behavior that oil (or pork bellies) prices display.