The intial conditions on the reservoir should be between zero and one. If the model is running correctly, the "population" should always remain between zero and one.
As a reintroduction to STELLA, let us consider a fun model with limited applications to biological systems. This is the second version of the logistic model which I call the Chaotic Logistic Model. This model is widely known and often used as the quintessential example of chaotic behavior in dynamical systems.
The difference equation is normally given in the form
X(i+1) = a*X(i)*(1-X(i))
where a is a parameter whose value is choosen to be between
zero and four.
This equation is not in a form which can be exploited by STELLA.
Instead, the change from one time to the next must be
explicitly determined. We can convert the usual chaotic logistic
model into the form needed by STELLA by doing the usual dirty trick,
subtracting X(i) from both sides of the equation. This gives
us:
X(i+1)-X(i) = a*X(i)*(1-X(i)) = a*X(i) - a*X(i)*X(i)
where the first term, a*X(i) is the inflow into the
population model, and a*X(i)*X(i) is the outflow.
The STELLA diagram for this model is:
The intial conditions on the reservoir should be between zero and one.
If the model is running correctly, the "population" should always
remain between zero and one.
This simple model displays many complex behaviors. For small values of the parameter a extinction is a stable equilibrium. For slightly largers values of a other stable equilibrium appear. As the value of a increases even further period doubling, a common feature of chaotic systems can be observed. Finally, for values of a greater than 3.87 true chaos is achieved.