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Building a predator-prey model in Minsky

The first step in building the Rabbits and Foxes model in Minsky is to insert two integral blocks on the canvas—one for Rabbits and the other for Foxes. An integral block is inserted by clicking on the \resizebox{!}{2ex}{\includegraphics{images/integrate}}% WIDTH=12 HEIGHT=14 operator. To alter its name from the generic ``int1'', either double-click on the widget, which brings up the context menu for integral blocks, or hover the mouse over the block and click the right-mouse button, and choose ``Edit'' to bring up the edit form (another method is to choose ``Rename all instances'' from the context menu). Name the two variables Rabbits and Foxes respectively, and you will have the following objects on your canvas:

\includegraphics{images/PredatorPreyRabbitsFoxesIntegralsOnly}% WIDTH=223 HEIGHT=191

As is typical of dynamic models, the rates of change of the variables Rabbits and Foxes depends on their current values. You therefore need to copy the variable names, which you do using the context menu command ``Copy item''. Do this and place both on the canvas:

\includegraphics{images/PredatorPreyRabbitsFoxes02}% WIDTH=451 HEIGHT=212

Next add the parameters that determine the rates of growth and death of the two species. The non-zero equilibrium is set by the zeros of $\left(r-\rho\times Foxes\right)$% WIDTH=226 HEIGHT=34 and $\left(-f+\phi\times Rabbits\right)$% WIDTH=277 HEIGHT=34 .

\includegraphics[width=\textwidth]{images/PredatorPreyRabbitsFoxes03ParametersAdded}% WIDTH=527 HEIGHT=297

Finally, the equations for the rates of growth of the two species are wired up, and the model can be simulated.

\includegraphics[width=\textwidth]{images/PredatorPreyRabbitsFoxes04Equations}% WIDTH=527 HEIGHT=563

If you don't want to display the complete equations on the canvas, you can use grouping to hide the complexity. The next figure illustrates several ways to use groups, and the feature that groups become transparent (and can be edited in situ) as the zoom level increases.

\includegraphics[width=\textwidth]{images/PredatorPreyRabbitsFoxes05Grouping}% WIDTH=527 HEIGHT=406


next up previous contents
Next: Building monetary models in Up: If you are experienced Previous: Minsky's unusual system dynamics   Contents