Introduction to Stella controls

The Stella graphical drawing area

Graphical view

In this simple diagram you can see some of the basic elements of a Stella model:

A stock is a pool of stuff

A flow is what makes the stock bigger or smaller

A converter is some factor that controls the flow.

A connector is an arrow indicating that one element controls another.

The little blob on the left side of the input flow is a source or sink outside the model.

Sometimes these flows represent an actual transfer of stuff from one place to another. Other times this is just an abstraction which represents some growth or decay process.

Equation View

By clicking the arrows at the top left you can switch from graphical view into equation view. If you double-click on any line of the equation you get a dialog box to edit the equation.

This model is very unformed and does not have any equations defined, except the relation between the stock and the input flow.

In general, you use the graph view to draw out general relations among the elements. Then you switch to equation view to fill in the details. There is also an interface view where you can put explanations, snazzy visuals, etc.

A simple flow model

	Here are the basic stocks and flows for a model of a college. We have simplified the model by not including transfer students.
	Let's suppose we are assuming that 20% of each class will drop out. This means that the dropout flow depends on the stock of students in each class. So, we need the connectors shown here.
	If we assume the other 80% of each class moves on to the next class, then that flow also depends on the stock of students.

The batted-ball model in Stella

In the batted ball model, velocity does not flow into position, but velocity does influence the change of position. So we model it like this.

Two simple population models

The exponential growth model

In the simplest population model, growth is a constant percentage of the population size.

The model has five elements:

The population size (a stock)
Births and deaths (flows into and out of popluation size)
The population birth rate (a converter, controlling births)
The population death rate (a converter, controlling deaths)

The logistic growth model

A standard population dynamics model is the logistic growth model. This model includes a carrying capacity, which is the largest population size the environment can support. The behavior of the logistic model is like this:

For small population sizes, the population grows exponentially;
As the population approaches carrying capacity, growth rate goes down and the population levels off.

The growth of the population in this model is controlled by the ideal growth rate , plus the carrying capacity.

Now, the growth rate depends on the population size relative to the carrying capacity.

An equation sometimes used is


                                                  Actual population size

   Actual growth rate = Ideal growth rate * (1 - ------------------------- )

						     Carrying capacity

This is a simple function which has the following nice properties:

For small population sizes, the growth rate is nearly the ideal growth rate
For larger population sizes, the growth rate is nearly zero.

In class we will work out these two examples on Stella. Pay special attention to how we create a graph pad object to graph the model results.