I'm trying to parametrically model a simple oscillating system representing supply based on production and consumption. The supply should graph something like a sine wave.
At any point in time, the change in supply should be equal to production minus consumption. Supply starts at 0. Both production and consumption scale relative to supply. In general, more supply means production decreases and consumption increases. For less supply it's the opposite. The intention is to get an oscillating supply from these values rather than one that's balanced.
I understand this is a very broad question, and there may be many solutions. But any information you can give me for understanding these kinds of problems (even just what topic or domain I'm in) would be much appreciated.
Look at Lotka-Verra equations. It assumes that the consumption rate is directly proportional to the abundance of products.