Vector plot does not take an equation as an argument

[Nusc]

VectorPlot[{D[x[t], t] == x[t] (4 - y[t] - x[t]^2),
D[y[t], t] == y[t] (-1 + x[t])}, {x, -10, 10}, {y, -10,
10}, {t, -10, 10}]

I'm trying to graph the phase plane of these equations. I get an error, what's wrong with my command?

 

[Dale]

Vector plot does not take an equation as an argument. You need to put the expressions in instead of the equations. Also, if you have the expression x[t] you cannot evaluate it at x=10 since that would be 10[t] which is going to throw an error. I think the correct command is:

VectorPlot[{x (4 - y - x^2), y (-1 + x)}, {x, -10, 10}, {y, -10, 10}, {t, -10, 10}]

 

[Nusc]

VectorPlot::nonopt: Options expected (instead of {t,-10,10}) beyond position 3 in VectorPlot[{x (4-y-x^2),y (-1+x)},{x,-10,10},{y,-10,10},{t,-10,10}]. An option must be a rule or a list of rules. >>

 

[Dale]

Oops, I missed that.

VectorPlot[{x (4 - y - x^2), y (-1 + x)}, {x, -10, 10}, {y, -10, 10}]

 

[Nusc]

How do I get mathematica to show the origin? it just fades in the middle.

 

[Dale]

Use the option

Axes->True

 

[Nusc]

What about the arrows that fade towards the y-axis

and how do I plot circles around the points (-2,0),(1,3),(2,0),(0,0)?

 

[Dale]

The arrows towards the y-axis appear to fade because VectorPlot plots both the magnitude and the direction of each vector, so a region with a lower magnitude is represented by shorter vectors. If you do not like this behavior you might consider using StreamDensityPlot instead of VectorPlot. Stream density plot shows the direction of the field using arrows and the magnitude using a background shading.

 

[Nusc]

Thanks for the help!

and how do I plot circles around the points (-2,0),(1,3),(2,0),(0,0)?

StreamDensityPlot[{x (4 - y - x^2),
y (-1 + x)}, {Circle[{-2, 0}, 1]}, {x, -10, 10}, {y, -10, 10},
Axes -> True]

StreamDensityPlot::nonopt: Options expected (instead of {y,-10,10}) beyond position 3 in StreamDensityPlot[{x (4-y-x^2),y (-1+x)},{Circle[{-2,0},1]},{x,-10,10},{y,-10,10},Axes->True]. An option must be a rule or a list of rules. >>

 

[Dale]

Unfortunately I am traveling and can't access Mathematica until thursday. However, if my memory is correct there is an option called Epilogue or something similar that you can use to plot any arbitrary list of graphics primitives. Try a search for "Epilogue" in the online help and if I misremembered the name then you will have to look through the list of options for StreamDensityPlot, Plot, and Graphics until you find it.