2
$\begingroup$

I'm new to Mathematica and I'm trying to plot the directional field of the following differential equation:

$$\dfrac{\mathbb{d}W}{\mathbb{d}R} = \dfrac{-0.02W + 0.00002RW}{0.08R-0.001RW}$$

And I was expecting to acheive the following results: enter image description here

So I tried to use StreamPlot in the following command:

StreamPlot[{1, (-0.02 W + 0.00002 R W)/(0.08 R - 0.001 R W)}, {R, 0, 3000}, {W, 0, 150}]

But It caused the following errors:

Power::infy: Infinite expression 1/0. encountered. >>
Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >>
Power::infy: Infinite expression 1/0. encountered. >>
Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >>

What am I doing wrong and how do I fix it?

|improve this question
$\endgroup$
  • 1
    $\begingroup$ Notice when R==0 and W==0 your denominator==0. Try {R,1,3000}, {W,1,150} and your 1/0 errors go away. That still leaves other issues, like your {1,(-0.02W+0.00002R W)...} when none of the examples in the help pages for StreamPlot use a 1 the way you do. Maybe you want {(0.08 R - 0.001 R W), (-0.02 W + 0.00002 R W)} but it is difficult to tell. $\endgroup$ – Bill Jan 21 '17 at 21:54
0
$\begingroup$

A couple tweaks improve the results.

1) @Rahul's myStreamPlot from here will fill in the streams nicely.

2) As @Bill writes, better to separate dW and dR in the plot command (otherwise the R direction will always have positive sign, which contradicts the predator-prey origin of the equations).

Together:

Options[myStreamPlot] = Options[StreamPlot];
myStreamPlot[f_, {x_, x0_, x1_}, {y_, y0_, y1_}, opts : OptionsPattern[]] := 
  With[{a = OptionValue[AspectRatio]}, 
  Show[StreamPlot[{1/(x1 - x0), a/(y1 - y0)} (f /. {x -> x0 + u (x1 - x0), y -> y0 + v/a (y1 - y0)})
  , {u, 0, 1}, {v, 0, a}, opts] /. Arrow[pts_] :> Arrow[({x0, y0} + {x1 - x0, (y1 - y0)/a} #) & /@ pts],
  PlotRange -> {{x0, x1}, {y0, y1}}]]

myStreamPlot[{(0.08 R - 0.001 R W), (-0.02 W + 0.00002 R W)}, {R, 0, 3000}, {W, 0, 150}]

Mathematica graphics

|improve this answer
$\endgroup$
  • $\begingroup$ I don't know, it works for me on 11.0.1. Try a fresh kernel? $\endgroup$ – Chris K Jan 22 '17 at 0:00
  • $\begingroup$ Thankx, I closed and reopened the program and tried again and it worked. Could you please add some explanation on how the code works, I'm a beginner in Mathematica . $\endgroup$ – razzak Jan 22 '17 at 0:30
  • $\begingroup$ Despite its name, myStreamPlot is not my work. To understand how it works, see the description by its author @Rahul here. $\endgroup$ – Chris K Jan 22 '17 at 1:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.