Economics Dynamics Problems 153

Economics Dynamics Problems 153 - = 4 + 2 r − r 2 >

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Discrete dynamic systems 137 Appendix 3.2 Two-cycle logistic equation using Maple > f:=x->r* x* (1-x); f : = x rx (1 x ) > > eq1:=f(f(x)); eq1 : = r 2 x (1 x )(1 rx (1 x )) > sol1:=solve(eq1=x,x); Sol1 : = 0 , 1 + r r , 1 2 r + 1 2 + 1 2 ± 3 2 r + r 2 r , 1 2 r + 1 2 1 2 ± 3 2 r + r 2 r > a1:=sol1[3]; a1 : = 1 2 r + 1 2 + 1 2 ± 3 2 r + r 2 r > a2:=sol1[4]; a2 : = 1 2 r + 1 2 1 2 ± 3 2 r + r 2 r > g:=diff(f(x),x); g : = r (1 x ) rx > eq2:=expand(subs(x=a1,g)*subs(x=a2,g)); eq2 :
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Unformatted text preview: = 4 + 2 r − r 2 > sol2:=solve(eq2=0,r); sol2 : = 1 − √ 5 , 1 + √ 5 > rstar:=sol2[2]; rstar : = 1 + √ 5 > evalf(subs(r=rstar,a1)); . 8090169946 > evalf(subs(r=rstar,a2)); . 4999999997 > evalf(subs(r=3.2,a1)); . 7994554906 > evalf(subs(r=3.2,a2)); . 5130445094...
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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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