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# Rossler attractor

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Rossler_Attractor.mws

Rossler Flow System - Rossler Attractor

by Yufang Hao, <yhao@student.math.uwaterloo.ca>

This worksheet contains the images of Rossler Attractor, and the animations which follows the trajectory.

 > restart; with(DEtools): with(plots):

```Warning, the name changecoords has been redefined
```

The Rossler attractor is defined by a set of three Differential equations:

x' =

y' =

z' = b +  -

where the coefficients a, b, and c are adjustable constants.

 > rosslerEqns := [ diff(x(t),t) = -(y(t)+z(t)), diff(y(t),t) = x(t) + a*y(t), diff(z(t),t) = b + x(t)*z(t) - c*z(t) ];

 > a:=0.17: b:=0.4: c:=8.5: DEplot3d(rosslerEqns, {x(t),y(t),z(t)}, t=0..300,          [[x(0)=0, y(0)=0, z(0)=0]],          x =-15..15, y=-15..15,z=-5..25,          stepsize=0.05, linecolour=1+sin(t*Pi/3)/2,          thickness=1, orientation = [-110,71]);

 > a:=0.17: b:=0.4: c:=8.5: display(   [seq(     DEplot3d(rosslerEqns, {x(t),y(t),z(t)}, t=0..4*i,          [[x(0)=0, y(0)=0, z(0)=0]],          x =-15..15, y=-15..15,z=-5..25,          stepsize=0.05, linecolour=1+sin((i-t)*Pi/5)/2,          thickness=2, orientation = [-110,71]),     i=1..25) # end seq   ], # end DEplot3d list insequence=true);

 > a:=0.17: b:=0.4: c:=8.5: display(   [seq(     DEplot3d(rosslerEqns, {x(t),y(t),z(t)}, t=0..4*i,          [[x(0)=0, y(0)=0, z(0)=0]],          x =-15..15, y=-15..15,z=-5..25,          stepsize=0.05, linecolour=1+sin((i-t)*Pi/5)/2,          thickness=2, orientation = [-110,71]),     i=1..25) # end seq   ], # end DEplot3d list insequence=true);

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