# 3d phase portrait for a system of DEs

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

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– Dr. belisarius
Dec 6 ’14 at 19:23

Can you show what you’ve tried?
– Dr. belisarius
Dec 6 ’14 at 19:24

It seems that your system diverges, that is, all trajectories run away.
– Alexei Boulbitch
Dec 6 ’14 at 19:38

1

@jens I seem to remember that phase plots were velocity against position.
– Sjoerd C. de Vries
Dec 6 ’14 at 20:43

1

@SjoerdC.deVries Terminology always depends on the context of the field. What you mean is a phase-space portrait.
– Jens
Dec 6 ’14 at 20:44

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1

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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]

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