VectorPlot or StreamPlot on a simplex

Questions
,
1

Hello,

I want to plot the solution to a system of the form

x'[t] == f[x,y,z,t]

y'[t] == g[x,y,z,t]

z'[t] == h[x,y,z,t]

in a triangular simplex, because x+y+z=1 and x>=0,y>=0 and z>=0.

Any ideas how to do that? I tried Vectorplot3D with a RegionPlot, but the resulting plot is not very compelling.

Thanks a lot for any help on this?

Clem

2

You can try the free package CurvesGraphics6, available from http://www.dimi.uniud.it/gorni/Mma
About half way through the page you will see an example of stream lines on a surface.

3

Thanks, Gianluca, I will look into that.

I meant something like in the following graph:

Koz3AP0.png
Koz3AP0.png521×466 24.1 KB

C

4

With the package and the code

region = DiscretizeRegion[Triangle[{{0, 0}, {1, 0}, {0, 1}}]];
PlotCurveOnSurface3D[{{x, y, 1 - x - y}, {x, y} \[Element] region},
 {{x, y}, {x, y} \[Element] region}]

you get the attached picture.