Re: instability in positive feedback systems.
A study of comparators as used in electronic systems is in order.
As to rails. They seem well illustrated in this graph. Obviously my previous numbers were wrong although the concept was correct.
Another good thing to study in this respect is subcritical multiplication in nuclear reactors and how delayed neutrons keep everything stable until you get into the prompt critical region. Now the climate boys claim "heat in the pipeline" (i.e. heat stored somewhere) keeps the system stable (i.e. acts like delayed neutrons in a reactor with a positive multiplication factor less than 1.0075.
So where is the heat in the pipeline? Climate scientists are still looking for it. If there is no delayed heat and the multiplication factor is above 1 the system is prompt unstable. Which is kina a bad thing. But it would have been noticed.
Control theory. Of which I know one or two things.
In any case stability at multiplication factors greatly over 1 is going to need a lot of explaining. And any multiplication of the 1C expected rise from CO2 doubling (gain = 1) of less than 2 (an additional 1C) is considered not too much of a problem. At least that is what the politicians at Copenhagen said.
And if the multiplication factor is .5 as some think? Very much no problem.
But I'm willing to wait for more data.