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Solving the problem with STELLA


STELLA is a program that allows you to solve systems of Ordinary Differential Equations without ever seeing the equations (which makes me sad). It has a slightly peculiar syntax but here we will work through one problems to show how to solve Equation (2). In the language of STELLA, our model will be made of Reservoirs, Flows and Converters. The reservoir holds the population N and is given an initial value (say 5). The flows hold the actual rate equations and say how the reservoir will change in time. There are three kinds of flow available: Inflows make the reservoir increase in value, outflows decrease the reservoir and bidirectional flows allow material to come in and out. Converters hold parameters and ancillary equations. To make everything work, all the variable held in different places need to be connected by arrows (I will show you how to do all this). Figure 2 shows the Stella version the first BioBomb model given in Equation (1) and has one reservoir (Population), an inflow (birth rate) an outflow (death rate) and two converters to hold the constants b and d. Obvious... isn't it?

Figure: 2 Stella versions of the BioBomb model tex2html_wrap_inline1024

Figure 3 shows the simpler model for the one parameter problem Equation (2). Note there is only one bi-directional flow which will let us make r be both negative and positive.

Figure: 3 Stella versions of the compact BioBomb model tex2html_wrap_inline1028

I will show you in class how to put these together and solve the equations. Figure 4 shows some sample STELLA output for a series of curves with r=0.2 and tex2html_wrap_inline938 . Compare Figure 4 with the behavior of the direction sets (Figure 1)

Figure 4: Example STELLA output for the problem of exponential growth for r=0.2 and initial conditions tex2html_wrap_inline938

next up previous
Next: Another way of visualizing Up: The Bio-Bomb Previous: Model Analysis

marc spiegelman
Mon Sep 22 21:30:22 EDT 1997