The Rossler Attractor

Clear["Global`*"]

<< Programm`RungeKutta`

?RungeKutta

Rossler Equation:
  
      x'  =  - (y + z)
      y'  =  x + 0.2 y 
      z'  =  0.2 + z (x - 5.7)                                 ` = d/dt

RungeKutta[ { -(y+z),
              x + 0.2 y,
              0.2 + z (x-5.7) },
            {x, y, z}, {0,0,0}, {50, 0.01} ];

Show[Graphics3D[Line[%]], Axes  ->  Automatic];

a  =  0.343b =   1.82c  =  9.75

\(NDSolve[
      \ {\(x'\)[t] == \(-\((y[t] + z[t])\)\), 

        		\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(y'\)[t] == \ x[t] + a\ y[t], 
        
		\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
        \(z'\)[t] == b + z[t]\ \((x[t] - \ c)\), 

        		\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x[0] == 0, y[0] == 0, 
        z[0] == \ 0}, 

      	\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {x, y, z}, {t, 0, 200}, 
      MaxSteps\  -> 10000\ , 
	\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 
      Method\  -> \ RungeKutta\ ]\)

\(\(ParametricPlot3D[Evaluate[{x[t], y[t], z[t]}\  /. \ %], 

      	\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {t, 0, 200}, \ PlotPoints -> 10000, 

      	\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Axes\  -> \ Automatic, 

      	\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ PlotRange\  -> \ {\(-10\), 70}\ ]\ ; \)\)

?? ParametricPlot3D