{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Economics Dynamics Problems 239

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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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:
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern