Re: the circle map

*To*: mathgroup at smc.vnet.net*Subject*: [mg52267] Re: the circle map*From*: p-valko at tamu.edu (Peter Valko)*Date*: Sat, 20 Nov 2004 03:41:36 -0500 (EST)*References*: <cneuml$qbc$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Roger, Can you tell me why is it that in the following code of yours: Clear[x, y, n]; a0 = 0.41209; 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] ; we get a fractal-like pic, but changing to a0 = 0.41208 we do not? (And why is that replacing Mod[-,1] by FractionalPart[-] in the above code will not give the same phenomenon? Peter Roger Bagula <tftn at earthlink.net> wrote in message news:<cneuml$qbc$1 at smc.vnet.net>... > 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

**Follow-Ups**:**Re: Re: the circle map***From:*DrBob <drbob@bigfoot.com>