Example 6. Solve
the Rössler attractor I. V. P.
with
,
with
,
with
.
Solution 6.
Enter the vector function
.
Compute the Runge-Kutta solution. Since this curve is known to twist a lot in 3D space, it will require about 1000 subintervals to get good resolution.
![[Graphics:../Images/LorenzAttractorMod_gr_315.gif]](../Images/LorenzAttractorMod_gr_315.gif)
We can plot the projections on the coordinate planes.
![[Graphics:../Images/LorenzAttractorMod_gr_323.gif]](../Images/LorenzAttractorMod_gr_323.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_327.gif]](../Images/LorenzAttractorMod_gr_327.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_331.gif]](../Images/LorenzAttractorMod_gr_331.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_335.gif]](../Images/LorenzAttractorMod_gr_335.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_338.gif]](../Images/LorenzAttractorMod_gr_338.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_341.gif]](../Images/LorenzAttractorMod_gr_341.gif)
We can plot the coordinate functions.
![[Graphics:../Images/LorenzAttractorMod_gr_344.gif]](../Images/LorenzAttractorMod_gr_344.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_347.gif]](../Images/LorenzAttractorMod_gr_347.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_350.gif]](../Images/LorenzAttractorMod_gr_350.gif)
![[Graphics:../Images/LorenzAttractorMod_gr_353.gif]](../Images/LorenzAttractorMod_gr_353.gif)
(c) John H. Mathews 2004