3d phase portrait for a system of DEs

Question

I'm trying to plot a phase portrait for a system of three differential equations
so could anybody help? example for :

          x'[t]=y[t]+x[t]
          y'[t]=y[t]z[t]+x[t]
          z'[t]=z[t]-x[t]-y[t]

I've tried using PhasePlot[] (package here) and ParametricPlot3D[] but couldn't achieve anything

Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the [faq]! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! — Dr. belisarius, Dec 06 '14 at 19:23
It seems that your system diverges, that is, all trajectories run away. — Alexei Boulbitch, Dec 06 '14 at 19:38
that system was just an example but i don't know how to plot a phase portrait for a given system od 3 ODEs so that's why i need help(i'm quite new to mathematica) — user23032, Dec 06 '14 at 19:41
StreamPlot handles 2D systems only (PhasePlot is not a Mathematica function). VectorPlot3D can plot the phase field. You will have to write your own function for plotting the phase curves (or find someone else's, if you can). (E.g., VectorPlot3D[{y[t] + x[t], y[t] z[t] + x[t], z[t] - x[t] - y[t]} /. v_[t] :> v, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}].) — Michael E2, Dec 06 '14 at 19:52
i found PhasePlot in a package called CurvesGraphics6 but i don't know how to use the solutions of the given system for plotting or how to plot trajectories — user23032, Dec 06 '14 at 19:55
With three variables wouldn't the phase space be 6 dimensional? How do you propose to visualize that? — Sjoerd C. de Vries, Dec 06 '14 at 20:31
@SjoerdC.deVries In the terminology of the linked package, phase plot just means a portrait of the flow in real space. — Jens, Dec 06 '14 at 20:36
@jens OK, didn't examine the package. Is that standard terminology? — Sjoerd C. de Vries, Dec 06 '14 at 20:38
@SjoerdC.deVries Yes, it's standard terminology in differential equations. — Jens, Dec 06 '14 at 20:40
@jens I seem to remember that phase plots were velocity against position. — Sjoerd C. de Vries, Dec 06 '14 at 20:43
@SjoerdC.deVries Terminology always depends on the context of the field. What you mean is a phase-space portrait. — Jens, Dec 06 '14 at 20:44

score 6 · Answer 1 · edited Apr 13 '17 at 12:55

Here is what I get using my answer to I'd like to display field lines for a point charge in 3 dimensions. You only have to copy the definitions from the first code block in that answer, and then enter this:

seedList = 
  With[{vertices = .1 N[PolyhedronData["Icosahedron"][[1, 1]]]}, 
   Join[Map[{#, 2} &, vertices], 
    Map[{# + {1, 1, 1}, -2} &, vertices]]];

Show[fieldLinePlot[{y + x, y z + x, z - x - y}, {x, y, z}, seedList, 
  PlotStyle -> {Orange, Specularity[White, 16], Tube[.01]}, 
  PlotRange -> All, Boxed -> False, Axes -> None], 
 Background -> Black]

field

The seed points in seedList can be adjusted to highlight different features, if desired.

3d phase portrait for a system of DEs

1 Answers1