Economics Dynamics Problems 95

Economics Dynamics Problems 95 - bp ) p } (with a = . 02...

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Continuous dynamic systems 79 PlotVectorField. Input (7) indicates some options that can be used with the Show command. These too could be employed in (a) above. Figure 2.9(b) (p. 46) Before we can plot the logistic function we need to solve it. In this example we shall employ the ±gures for a and b we derive in chapter 14 for the UK population over the period 1781–1931. a = 0 . 02 and b = 0 . 000436 and with p 0 = 13. (1) Input <<Graphics`PlotField` (2) Input DSolve[{p’[t]==(0.02-0.000436p[t])p[t], p[0]==13}, p[t], t ] (3) Input logistic=%[[1,1,2]] (4) Input logplot=Plot[logistic, {t,0,150} ] (5) Input arrows=PlotVectorField[{1,0.02p-0.000436p^2}, {t,0,150}, {p,0,50} ] (6) Input Show[logplot, arrows, AxesOrigin->{0,0}, AxesLabel->{"t","p"} ] Note again that the PlotVectorField has the ±rst element in the form { 1 , ( a
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Unformatted text preview: bp ) p } (with a = . 02 and b = . 000436). Appendix 2.2 Plotting direction felds or a single equation with Maple Figure 2.8 (p. 45) Given the differential equation dy dx = 2 x y the direction eld and isoclines can be obtained using Maple as follows: Step 1 Load the DEtools subroutine with the instruction with(DEtools): Note the colon after the instruction. Step 2 Dene the differential equation and a set of points for the isoclines. Eq:= diff(y(x),x)=2*x-y Points:={[-2,2],[-1,1],[-1,0.5],[-0.5,-2], [0,-2],[0.5,-1.5],[0.5,-1],[1,-1],[1.5,-0.5]}; Step 3 Obtain the direction eld and the integral curves with the instruction DEplot(Eq,y(x),x=-2. .2,Points,y=-2. .2, arrows=slim, linecolour=blue);...
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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.

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