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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)=1y(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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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.
 Fall '11
 Dr.Gwartney
 Economics

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