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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)

y' = x+a*y

z' = b + x*z  - c*z

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) ];

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]);

[Maple Plot]

>    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);

[Maple Plot]

>    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);

[Maple Plot]

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