This is cute.
(from the 0hedge comments)
Punchline is, have you ever noticed how a plot of human population over just 4000 years looks like a dirac-delta function? That is, the input we’re all trying to predict the response of.
on Mon, 09/20/2010 – 22:41
I’m guessing the Dirac delta spike happened around 1850 and still hasn’t come back down? Before this it was flat-line near zero?
But now that I say this, deltas overshoot on return, yes?
on Mon, 09/20/2010 – 23:00
In theory, a dirac delta function shoots to infinity instantaneously then just as quickly returns to zero.
In nature, the function is approximated and approaches some really high value faster than exponentially, then returns just as fast.
So you were correct in your inference, up until you said overshoot. The dirac input returns exactly to zero (things like a population, are absolute) almost always cause linear, causal, systems to overshoot, then snap back with some degree of undershoot – then oscillate until either a new equilibrium is reached – ie a steady state, or some degree of infinite instability. Some forms of this instability, I’m sure could be called what you label, ‘bifurcation’.
…but I’m no PHD. Muti-variable control theory goes deeper than, say, the rabbit hole.