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Economics Dynamics Problems 206

Economics Dynamics Problems 206 - 190 Economic Dynamics...

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190 Economic Dynamics solutions. These are invariably employed for systems of nonlinear differential equation systems. 4.12.1 Direction fields and phase portraits with Mathematica Direction fields in Mathematica are obtained using the PlotVectorField command. In order to use this command it is first necessary to load the PlotField package. There is some skill required in getting the best display of direction fields using the PlotVectorField command, and the reader should consult the references supplied on using Mathematica in chapter 1. Given the system of differential equations (4.35), then a direction field can be obtained with the instructions Needs[``Graphics`PlotField`’’] dfield=PlotVectorField[{f(x,y,t),g(x,y,t)}, {x,xmin,xmax}, {y,ymin,ymax}, DisplayFunction->Identity] Show[dfield, DisplayFunction->$DisplayFunction] To obtain a ‘good’ display it is often necessary to adjust scaling, change the arrow lengths and change the aspect ratio. All these, and other refinements, are accomplished by optional instructions. Thus, figure 4.36(a) can be obtained from
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