Martin Schaffernicht wrote:I've also taken notice that the number of apparent feedback loops changes according to how many or few auxiliary variables one uses to formulate the problem.
The word "apparent" is important in your sentence, Martin. Feedback has to do with stocks and flows only. To see the real dynamic links in a model, you should remove all auxiliaries and have just one flow per stock. (Put auxiliary equations into the flow equations, and merge multiple flows of a stock into one).
When this is done, you have feedback through a stock if and only if there is a direct or indirect dependency path from the stock back to its own (net) flow
Adding auxiliaries does not create more loops; it just creates more detail to the paths from stocks to flows. (Paths that do not start from a stock and end at a flow can be removed completely when you study feedback).
Even with the above simplifications, the number of feedback loops gets overwhelmingly large even for relatively small models. The art of finding the dominant loops is therefore a key to making any sense out of the loops. I write "art", because I am not aware of any robust scientific solutions, technical implementations, and graphical visualization for to solving this problem among the current simulation tools. (There are some "toy" solutions around, but much research and development is still to be done in this area).