Would not an oscillation in debt require a feedback loop and a gain of greater than one, as in classical control theory?

I know there are other theoretical modes that can drive oscillatory behavior, but I can't see what would drive a debt oscillation other than such a feedback loop consisting of changes in interest rate, regulation, and behavior. Likely any such oscillation would be on a very long scale -- to the tune of decades. Perhaps there is short-duration cycle overlaid upon a much larger generational cycle?

I am sure that there have been attempts to model economic theory in terms of overdamped and underdamped systems, with various input functions and signal paths, but the complexity would likely be intractable. A discrete simulation with enough interconnected but independently acting entities might be viable.

I imagine that social mores and emotional readings like "consumer confidence" play into any such mechanism, but maybe those could be quantified in some way as well.