Is this a new strange attractor?

Question

I recently made some experiments in programming strange attractors, and I found this (very simple) equations, which create a nice strange attractor:

xn=x+dt*(z-y)
yn=y+dt*(x/2-1)
zn=z+dt*(-xy/2-z)

You can see it in action on my Youtube channel: https://youtu.be/Bm_M6mUGjtg

My question: Is this a variation of the Lorenz- or Rössler attractor - or did I stumble upon something new?

---

EDIT:

Meanwhile I programmed a little 3D View for this attractor:

You can see/move the view on this applet (Java needed): https://cerumen.de.cool/attractor/index.html (Here you also find the source code for Processing)

And here the Javascript-Version: https://cerumen.de.cool/attractor/js/index.html (with processing.js... bit slow)

Perhaps my question was also asked too amateurishly. I was simply surprised by the simplicity of the system of equations I have found.

Therefore I would like to know if this strange attractor is a descendant of one of the well known ones (Lorenz / Rössler).

---

Edit 2:

I have now brought the system of equations into a more general form:

xn=x+dt*(z-y)
yn=y+dt*(ax-b)
zn=z+dt*(-axy-z)

with a in range [0 to 1], b in range [0.5 to 1]

This makes it more interesting. Here some sample images for different values for a and b:

---

Edit 3:

Here a video with the generalized equations and constantly changing parameters a and b: https://youtu.be/gxusM8pmNwU

I think you can see here quite well how the system goes from order through bifurcation into chaos...

Answer 1

I just figured I added some Mathematica code and a picture for the attractor in the question.

With[{dt = 0.001},
  iter[{x_, y_, z_}] := {x, y, z} + 
    dt {(z - y), x/2 - 1, -x y/2 - z} 
  ];
pts = NestList[iter, {0.1, 0.1, 1/2}, 500000];
ListPlot[{#1, #2} & @@@ pts[[1 ;; ;; 5]], PlotRange -> All, 
 Axes -> False, PlotStyle -> {Opacity[0.9], PointSize[Tiny], Orange}, 
 AspectRatio -> 1, Background -> Gray, ImageSize -> {800, 600}]

I only plotted every fifth of the points, as it is a bit quicker, and the image is a bit more pleasant with this variant.

EDIT:

With some more creative edits, $$ (x_{n+1}, y_{n+1}, z_{n+1}) =(x_n, y_n, z_n)+dt (z - y, -1 + x + 6 \sin(\pi/4 + 10 x/ z), -x y/2 - z) $$ one can produce the following picture. Adding any non-linear disturbance, and making sure that it does not diverge, or converge to something boring, it is rather easy to cook up exotic variations that give rise to chaotic behavior.

Answer 2

In another forum a user drew my attention to the publication of

• J. C. Sprott, Some simple chaotic flows, Phys. Rev. E 50, R647-R650 (1994), doi:10.1103/PhysRevE.50.R647, author pdf.

This shows that there are many very simple chaotic systems of equations.

I guess this answers my question...

You can see some of the equations here, and here are the corresponding graphs.

But thank you all for your interest.