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Economics Dynamics Problems 239

# Economics Dynamics Problems 239 - y:=proc(t option remember...

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Discrete systems of equations 223 with Maple , then the last line becomes plot(data, plotstyle=point); The resulting trajectories are similar to that shown in the chart in figure 5.2 (p. 221). As one might expect, both Mathematica and Maple allow more control over the display of the trajectories than is available within Excel . Furthermore, both these programmes allow more than one trajectory to be displayed on the same diagram. This is not possible within spreadsheets. Spreadsheets can display only one ( x , y )- trajectory at a time. Example 5.9 (cont.) The input instructions for each programme for producing discrete plot trajectories are Mathematica Clear[x,y,t,a,b] x[0]:=0.01; y[0]:=0; a:=1.4; b:=0.3; x[t - ]:=x[t]=1-a x[t-1]^2+y[t-1] y[t - ]:=y[t]=b x[t-1] data=Table[{x[t],y[t]},{t,0,20}]; ListPlot[data,PlotJoined->True,PlotRange->All] Maple t:=’t’: x:=’x’: y:=’y’: a:=’a’: b:=’b’: x:=proc(t) option remember; 1-a*x(t-1)^2+y(t-1) end:
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Unformatted text preview: y:=proc(t) option remember; b*x(t-1) end: x(0):=0.01: y(0):=0: a:=1.4: b:=0.3: data:=[seq([x(t),y(t)],t=0. .20)]; plot(data); The resulting trajectories are similar to that shown in the chart in fgure 5.3. Spreadsheets do not allow three-dimensional plots, but it is very easy to adapt the instructions just presented For Mathematica and Maple to do this. The only essentialdiFFerenceisthefnallineineachprogramme.Assuming‘data’recordsthe list oF points { x ( t ) , y ( t ) , z ( t ) } , then a three-dimensional plot requires the instruction Mathematica ListPlot3D[data,PlotJoined->True] Maple plot3d(data); 5.6 The stability of discrete systems 5.6.1 Real distinct roots ±or systems with real distinct roots, r and s, which thereFore have linearly inde-pendent eigenvectors, we can establish the stability properties oF such systems by...
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