The Rossler Attractor

Manipulate[
Module[{f={X,Y,Z}/.Quiet[NDSolve[SetPrecision[{
X'[t]==-(Y[t]+Z[t]),
Y'[t]==X[t]+a Y[t],
Z'[t]==b+X[t]Z[t]-c Z[t],
X[0]==1,Y[0]==1,Z[0]==1},8]/.{a->aval,b->bval,c->cval},
{X,Y,Z},{t,0,maxt},PrecisionGoal->8,WorkingPrecision->8]][[1]],
l={X[t],Y[t],Z[t]}},
Grid[{{Column[Table[Plot[f[[i]][t],{t,0,maxt},PlotRange->All,
PlotStyle->Prepend[{Which[i==1,Red,i==2,Orange,i==3,Blue]},Thick],ImageSize-> {150,100},
AxesLabel->TraditionalForm/@{t,l[[i]]},ImagePadding->{{45,10},{10,25}}],{i,3}]
],ParametricPlot3D[Evaluate[#[t]&/@f],{t,0,maxt},BoxRatios->{1,1,1},PlotRange->All,AxesLabel->TraditionalForm/@l,ColorFunction-> "Rainbow",PlotStyle-> Thick,ImageSize-> {350,300},PerformanceGoal->8,PlotPoints->4,MaxRecursion->8,ImagePadding->25]}}]],
{{maxt,40,"max t"},10,40,1},
{{aval,.2,"a"},.1,.4,.01,Appearance-> "Labeled"},
{{bval,.2,"b"},.1,1,.1,Appearance-> "Labeled"},
{{cval,8,"c"},1,10,.1,Appearance-> "Labeled"},SynchronousUpdating->False]

The Rossler Attractor is a simple kind of dynamic system with interesting behavior. You can vary the parameters of the constants a, b, and c in time.

The system is defined by:

((d x)/(d t))==-(y+z),

((d y)/(d t))==x+a y,

((d z)/(d t))==b+x z-c z.

H.-O. Peitgen, H. Jürgens, D. Saupe, Chaos and Fractals: New Frontiers of Science, 2nd ed., New York: Springer, 2004.

Contributed by: Daniel de Souza Carvalho

Based on a program by: Eric W. Weisstein