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Question: Phase Portrait Showing attractor

Question:Phase Portrait Showing attractor

bongiman 133 Maple
plot student
July 07 2008
0

Hi, i am wondering if someone can help me with the Maple code below? I am trying to plot a phase portrait for the below map

x[n+1]:= exp(y[n])
y[n+1]:= ln(x[n]^alpha)-y[n]^2+Beta

However when i execute my code my computer goes nuts and evaluates it for what seems to be eternity. I'm certain there is soemthing wrong with my code coz it really shouldn't be takin more than an hour to run it. I have a fairly decent spec machine so i know it's not that. Below is my code:

>N:=20000;
> xa:=-10: ya:=-10:
> xb:=10: yb:=10
> x0:=0: y0:=0:
> alpha:=0.4: Beta:=1.2:
> H:=proc()
> global x0,y0,x1,y1, a,b;

> x1:= exp(y0); y1:=ln (x0^(alpha))-y0^(2)+Beta;

> x0:=x1; y0:=y1;
> [x0,y0]
> end proc:
> from 1 to 99 do H() end do:
> orbit:= [seq(H(),k=100..N)]:

> plots[pointplot](orbit,symbol=point, view=[xa..xb,ya..yb],colour=black, title=sprintf("StrangeAttractor:a=%a,b=%a",a,b));

Thanks
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