Economics Dynamics Problems 151

Economics Dynamics Problems 151 - portant in using this to...

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Discrete dynamic systems 135 Neither Mathematica nor Maple , however, can solve directly the logistic equation y t + 1 = (1 + a ) y t 1 + by t This is readily accomplished using the substitution provided in section 3.9. It is worth pointing out that in the case of numerical examples, if all that is required is a plot of the sequence of points, then there is no need to solve the recursive (or difference) equation. We conclude this section, therefore, with simple instructions for doing this. 14 The equation we use as an example is p t = 5 . 6 0 . 4 p t 1 p 0 = 1 Mathematica Clear[p]; p[0]=1; p[t - ]:=p[t]=5.6-0.4p[t-1]; data=Table[{t,p[t]},{t,0,20}]; ListPlot[data,PlotJoined->True,PlotRange->All]; Maple t:=’t’: p:=’p’: p:=proc(t)option remember; 5.6-0.4*p(t-1)end: p(0):=1: data:=seq([t,p(t)],t=0. .20)]; plot(data,colour=black,thickness=2); Notice that the instructions in Maple require a ‘small’ procedural function. It is im-
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Unformatted text preview: portant in using this to include the option remember, which allows the programme to remember values already computed. Higher-order recursive equations and nonlinear recursive equations are dealt with in exactly the same way. With discrete dynamic models, however, it is often easier and quicker to set the model up on a spreadsheet (see Shone 2001). Appendix 3.1 Two-cycle logistic equation using Mathematica THEOREM The number a satisfes the equation a = F ( F ( a )) iF a is either a fxed point or is part oF a two-cycle For the dynamical system x n + 1 = F ( x n ) 14 I am grateful to Johannes Ludsteck, Centre for European Economic Research (ZEW), for the method of computing tables from recursive equations in Mathematica , which is more efFcient than the one I provided in the Frst edition....
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