#### Exponential Decay - Alternative Goal Seeking Template

##### Amrit Thomas

- 1 year 2 months ago

#### 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.

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.

- 5 years 4 months ago

#### Shaping Our Healthier Futures Template

##### Geoff McDonnell ★

This will be the template for the Shaping Our Healthier Futures thread models. If you haven't previously reviewed the Adventures in Wonderland concept please do so as wandering in this environment is likely to make a lot more sense afterwards.

- 8 years 2 months ago

#### Collaborative Model Building Template

##### James Houghton

This is a template for collaborative model building, which explains a little bit about the modeling process to get everyone up to speed on what we're doing and why we're doing it.

- 8 years 4 months ago

#### Template Mind Map

##### Poppy Richardson

I've put "New Stock"s at the edges to expand it to allow more freedom of space when working

- 5 years 1 month ago