Thanks all for the patience and for pointing to the main principles of feedback, so I can take it from there. Vanesch shows how the total gain of a feedback process can be calculated in a steady state
but in reality we are looking at constant dynamic transients, as the forcings functions of climate are constantly changing. The process reacts to that with the gain factor A, but with a certain delay, in climate ranging from minutes to centuries perhaps. Feedback uses (part) of the (delayed) output of a process as input and has it's own inertia and gain factor B.
To illustrate what happens when introducing a delay, I have made a very modest little model of the most simplest feedback that uses a step of one to simulate total delay from proces imput to the arrival of the feedback signal to be added or subtracted to the next system input (see attachment). I hoped to be able to use an older version I made a few years ago but I was out of luck so I had to make it again.
As input we use a one dimensional random walk (column C) and we compare the reaction in a zero feedback process (column D) with a gain A (cell C2) , a positive feedback process (column D) with the factor B (cell C3) and a negative feedback process with the factor -B in column F.
Let's look at a certain output, the first 100 steps, with A = 1 and B = 0.5 (green cells)
We see the average
total gain for the feedbacks (in steady state pos:2, neg 0.67) are close (2.13 and 0.62). So that's fine. We also count the number of signal reverses for n=1000. The random walk makes 528 reverses (from a positive to a negative step or vice versa), which is close to the expected average of 0.5n = 500. But we see that the positve feedback process makes less reverses (344) and the negative feedback makes more reverses (640). This is obvious and important, as the added previous positive feedback steps tends to increase the deviation from to zero persistently
(instable), whereas the negative feedbacks tends to pull the process back to the zero mark (stable) anti-persistent
. Because of that we also see that the red positive feedback process is smoother and the negative feedback process is more jerky.
Before the all revealing playing with the parameters it's maybe better to see if we didn't lose everybody/anybody. Still here?