Economics Dynamics Problems 208

Economics Dynamics Problems 208 - 192 Economic Dynamics...

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Unformatted text preview: 192 Economic Dynamics Figure 4.37. 4.12.2 Direction fields and phase portraits with Maple Direction fields and phase portraits are more straightforward in Maple and use the same basic input commands. Given the system of differential equations (4.35), then a direction field can be obtained with the instructions with(DEtools): with(plots): Dfield:=dfieldplot( [diff(f(x(t),t)=f(x(t),y(t),t), diff(y(t),t)=g(x(t),y(t),t)], [x(t),y(t)], t=tmin..tmax, x=xmin..xmax, y=ymin..ymax); display(Dfield); Notice that the instruction ‘with(plots):’ is required for use of the display command. To obtain a ‘good’ display it is often necessary to add options with respect to arrows. For example, a Maple version of figure 4.36(a) can be achieved with the following input with(DEtools): with(plots): Dfield:=dfieldplot( [diff(x(t),t)=1-y(t),diff(y(t),t)=x(t)^2 +y(t)^2], [x(t),y(t)], t=0..1, x=-2..2, y=-1..3, arrows=SLIM): display(Dfield); The phase portrait, not surprisingly, uses the phaseportrait command of Maple. This particular command plots solution curves by means of numerical methods. ...
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