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MathGroup Archive 2004

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the circle map

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52249] the circle map
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Wed, 17 Nov 2004 02:20:18 -0500 (EST)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

I've done a lot of searches on chaos
 and Mathematica and have never seem this.
It is sensative chaos , in both the angle based a0 and the
initial starting point.
The circle was used by Chua as a starting point in his lectures on Chaos.

Clear[x,y,a,b,s,g,a0]
(* circle map: from  Chaos in Digital Filters ,Chua,Lin,
  IEEE transactions on Circuits and Systems,vol 35 no 6 June 1988*)
  (* very sensitive to intial conditions*)
a0=Cos[Pi/6]/2;
x[n_]:=x[n]=Mod[-a0*x[n-1]-y[n-1],1]
y[n_]:=y[n]=Mod[x[n-1],1]
x[0]=0.7;y[0]=.65;
a=Table[{x[n],y[n]},{n,0, 10000}];
ListPlot[a, PlotRange->All]

Respectfully, Roger L. Bagula

tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at netscape.net
URL :  http://home.earthlink.net/~tftn


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