A couple of months ago, in-between jobs, I was doing some light research work at Cornell and sitting in on some classes (hiding behind a Big Red hoodie) when a graduate student offhandedly introduced the class to system dynamics and continued rambling on. I knew immediately that that was what I wanted to do.(adsbygoogle = window.adsbygoogle || []).push({});

I graduated a year ago with a degree in information technology and minors in math and econ. More than anything I enjoyed graph theory, microeconomics, data mining, probability, database design, etc... but looking back on it I realize I honestly just loved modeling things! Turning a shopping site into its component tables or determining the games firm play when in direct competition with one another--really anything involving coming up with a well-defined representation of a complex real-worldthing. Everything else was just going through the motions.

Since then I've looked into system dynamics (stocks and flows and such) and one thing worries me. Whenever a fishery is mentioned (and man, do system dynamics textbooks love their fisheries) and a section details how some stock of fish f(t) is making fishy love and growing at a rate of r*f(t), it is always accompanied by a screenshot of a red curve in some computer program. I'm willing to bet this line is being created by taking teensy-tiny timesteps and incrementing the stock of fish bit by bit. Why is an equation not given? Why does the book not mention that this model can be reduced to the equation f(t) = f(0) * e^rt ? No computer needed!

So here is where you can help: What field of math would provide the methodology for determining which models could be "equationized", and what tools would be used in distilling a model to simple equations dependent only on t? It would be great if this is exactly what's to come from delving deeper into system dynamics, but I definitely don't want every model to be resolved by putting it into a computer, pressing the "Run" button, and seeing what number pops up. Where's the fun in that? Since elementary school the mantra has always been, "Simplify, simplify, simplify!"

And if nothing you read above makes sense, you can still help me here:

Suppose that same stock of fish is leveling off due to an overcrowding effect. There are still fish born every day, but fewer as the days go on. Suppose that the rate of growth of the stock of fish f(t) can be represented as r/f(t) for r > 0 at any point in time t. How could this be reduced to a simple equation dependent only on t (and an initial value at t=0, of course), what tools would you use to do it, and where can I learn more!?

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# System dynamics but with math - guidance needed!

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