# How can I plot 3-D system

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.

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}
]

• 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. Sep 27, 2020 at 7:54

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"]


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.

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