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Vectors and fixed points in a 3D plot

Posted 10 years ago
ContourPlot3D[{0 == (2*2*0.5)/(1 + w^2) - 1/30 v Log[2],
  0 == (u^2 *0.5)/(1 + u^2) - 1/120 w Log[2]}, {u, 0, 30}, {w, 0,
  100}, {v, 0, 2}, AxesLabel -> Automatic,
ContourStyle -> {Cyan, Red}]
Hello, i have this code that creates a 3D plot. I want to see the vectors and the fixed points in the plot. How is this possible?
Thank you.
11 Replies
Thank you very much. If i want bigger scale for the u axis arrows, then i will have to increase the number from 10 to 30 for example, right?
If I understand correctly, you have a 3D vector field defined by:
{-u v + (u^2 *0.5)/(1 + u^2) - 1/120 u Log[2],
  (u^2 *0.5)/(1 + u^2) - 1/120 w Log[2],
   (2*2*0.5)/(1 + w^2) - 1/30 v Log[2]}
 In that case you would plot a vector field of this with the commad:
vectors= VectorPlot3D[{-u v + (u^2*0.5)/(1 + u^2) -
   1/120 u Log[2], (u^2*0.5)/(1 + u^2) -
   1/120 w Log[2], (2*2*0.5)/(1 + w^2) - 1/30 v Log[2]}, {u, 0,
  10}, {w, 0, 100}, {v, 0, 2}, VectorScale -> 0.003]

You can combine this with your surface plot:
surface =
ContourPlot3D[{0 == (2*2*0.5)/(1 + w^2) - 1/30 v Log[2],
   0 == (u^2*0.5)/(1 + u^2) - 1/120 w Log[2]}, {u, 0, 30}, {w, 0,
   100}, {v, 0, 2}, AxesLabel -> Automatic,
  ContourStyle -> {Lighter@Cyan, Lighter@Red}];

Show[surface, vectors]
POSTED BY: Sean Clarke
ContourPlot3D[{0 == -u v + (u^2 *0.5)/(1 + u^2) - 1/120 u Log[2],
  0 == (u^2 *0.5)/(1 + u^2) - 1/120 w Log[2],
  0 == (2*2*0.5)/(1 + w^2) - 1/30 v Log[2]}, {u, 0, 10}, {w, 0,
  100}, {v, 0, 2}, AxesLabel -> Automatic,
ContourStyle -> {Yellow, Red, Cyan}]
well we have these 3 odes. the first one is du/dt , the second one is the dw/dt and the last dv/dt. I put them equal to zero to draw the nullclines. After this, as i have the 3D plot of all these equations, i want to see the flow in order to examine the type of the fixed points. If they are stable/unstable. is it more clear now? sorry if i confused you, but i am not familiar with using the software. Thank you!
In order to plot the vector field, we need equations for the vector field. If you're not sure what the equations are for the vector field, please try describing where the vector field comes from and maybe we can figure out what the equations should be. 

I could invent a random vector field to put on this surface. There are infinitely many vector fields I could put on your example surface. 

I can't help plot the vector field if we don't have equations for the vector field. 
POSTED BY: Sean Clarke
or for example when we have the toggle switch

http://2008.igem.org/wiki/images/thumb/6/6f/UCSFmodel_nullclines.png/800px-UCSFmodel_nullclines.png

and we can find the stability of the cross points, by using the arrows. i want something similar but in 3 dimensions


for example this one. i want something similar
Please first define the vector field. 

What is the vector field you want to work with?
POSTED BY: Sean Clarke
i am not sure if i say it right, sorry about that, but i want to see the arrows how they behave with the fixed points. how they approach the fixed points in order to find the stability of them
The first step is to define the flow you want to visualize. That is, create a function, let's call it f where f[{u,v}] is the vector for the flow you want. 

What is the flow you are trying to visualize?
POSTED BY: Sean Clarke
I'm not sure I understand. What do you mean by "the vectors"? Are you looking to draw a vector field on these surfaces? If so, how do you define the vector field?

Are the vectors the gradient of the parameterization? 
POSTED BY: Sean Clarke
I am looking to draw the arrows that show us the direction of the flow
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