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If I have three equations nonlinear. I need to see the behavior around (0,0). How do I plot the three-dimensional system? Thank you in advance.

enter image description here

I try to use this code

ParametricPlot3D[
 {2 x^2, -y^2, z^2}, 
 {u, 0, 2 Pi}, {v, 0, 2 Pi},
 PlotStyle -> {Red, Green}
 ]
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    $\begingroup$ If you solve these differential equations (e.g. DSolve[x'[t] == 2 x[t]^2, x, t]) you will get solutions with a constant in each of them. To find the constant, you must have some initial condition. Otherwise you can't plot the system. $\endgroup$
    – C. E. ♦
    Commented Sep 27, 2020 at 7:54

1 Answer 1

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Your differential equation describes a vector field (velocity field) that you may display e.g. using SliceVectorPlot3D:

SliceVectorPlot3D[{2 x1^2, -2 x2^2, 
  3 x3^2}, "CenterPlanes", {x1, -.1, .1}, {x2, -.1, .1}, {x3, -.1, \
.1}, PlotTheme -> "Scientific"]

Velocity Field

You see, that e.g. a particle coming from below from {0.1,-0.1,-0.1} with velocity {0.02,-0.02,0.03} will turn into the direction {1,-1,0} and will never reach the x3==0` plane.

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  • $\begingroup$ Shouldn't it be -1 x2^2? $\endgroup$
    – Lee
    Commented Sep 27, 2020 at 16:03
  • $\begingroup$ Thank you Daniel Huber, How do I make the shape move in place until I see the back parts $\endgroup$
    – user74531
    Commented Sep 27, 2020 at 17:07
  • $\begingroup$ @user74531 Simply click on the graphics and move the mouse. $\endgroup$
    – Daniel Huber
    Commented Sep 28, 2020 at 8:19
  • $\begingroup$ @Lee Yews you are right, thank you. $\endgroup$
    – Daniel Huber
    Commented Sep 28, 2020 at 8:21

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