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Ceiling Template

Benjamin David Hendricks
A template to be used when a stock metrically can't grow beyond a certain point---e.g. a 0-10 psychometric scale. 
The technique used to address the problem is based on Zeno's paradox, where Achilles is unable to reach a finish line because he must first cross half the distance, then half the remaining distance, ad infinitum. Likewise, this system reduces the growth rate proportionately to how close the stock is to the defined ceiling.
Parameters include the base growth rate (the rate at which the stock increases before the system's balancing loop activates), the ceiling, the initial value of the stock, and a "tolerance point." This is the point at which the system decides to intervene to prevent the stock from passing the ceiling, and begins to reduce the growth rate. Raising the tolerance of the system gives the base growth rate more dominance over the behavior graph while sharpening the negative curve at the top of the S-curve.
A note concerning simulation---only Runge-Kutta will calculate the appropriate behavior. Using Euler will result in oscillations around the ceiling.

Template Archetype

  • 5 years 4 months ago