Rössler Attractor

Author

Eric W. Weisstein
September 5, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DynamicalSystems/RoesslerAttractor.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RoesslerAttractor.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Numeric Solution

f={X,Y,Z}/.NDSolve[{
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}/.{a->.2,b->.2,c->8},
{X,Y,Z},{t,0,50}][[1]]

Plots

<<Graphics`Colors`

Solutions along each axis

l={X[t],Y[t],Z[t]};
Show[GraphicsArray[Table[Plot[f[[i]][t],{t,0,50},PlotRange->All,
PlotStyle->Red,
AxesLabel->TraditionalForm/@{t,l[[i]]},DisplayFunction->Identity],{i,3}]
]]

Attractor

ParametricPlot3D[Evaluate[Append[#[t]&/@f,Red]],{t,0,50},BoxRatios->{1,1,1},PlotRange->All,PlotPoints->1500,AxesLabel->TraditionalForm/@l]