Using StreamPlot and Manipulate to show the field lines with varying the parameters

Question

I have the equation $$\dot{x}=F(x(t);\mu,\lambda)=\mu x-\lambda x^2+3$$ and I want to use StreamPlot and Manipulate to vary $\lambda$ and $\mu$.

The code for an example how it should look like:

Manipulate[
StreamPlot[{y, -λ - μ x + x^3}, {x, -3, 3}, {y, -3, 3}, 
   StreamScale -> Large, 
   PlotLabel -> Row[{"λ = ", λ, " ,  μ = ", μ}]], 
{λ, -1, 1}, {μ, -1, 1}]

So why use a StreamPlot, which displays functions of two variables ($x$ and $y$)? — David G. Stork, Mar 16 '17 at 18:47
Is there any other possibility to show the field lines with varying $\lambda$ and $\mu$? And when I use $y$ for a Dummy? — Manu, Mar 16 '17 at 18:48
It makes no sense to use $y$ for a "dummy". You can plot ${\partial x \over \partial t}$ versus $x$. (See solution.) — David G. Stork, Mar 16 '17 at 18:51

score 2 · Accepted Answer · answered Mar 16 '17 at 18:51

2

The problem as stated makes little sense. A StreamPlot shows $y$ and $x$. If you let the horizontal axis be $x$ and the vertical be the derivative of $x$, then:

Manipulate[
 StreamPlot[{x, -λ x^2 + μ x + 3}, 
    {x, -3, 3}, {y, -3, 3},
    StreamScale -> Large, 
    PlotLabel -> Row[{"λ = ", λ, " ,  μ = ", μ}]], 
  {λ, -1, 1}, {μ, -1, 1}]

answered Mar 16 '17 at 18:51

David G. Stork

41,180
3
34
96

I tried it with
```
`Manipulate[StreamPlot[{y, -λ x^2 + μ x + 3}, {x, -3, 3}, {y, -3, 3},
StreamScale -> Large, PlotLabel -> Row[{"λ = ", λ, " ,  μ = ", μ}]], 
{λ, -1, 1}, {μ, -1, 1}]`
```
I want to characterize my equlibrium points with analysing the and direction of the field lines, and this only possible when I use $y$ instead of $x$ in your code... I dont know if this make sense, but I get my fieldlines.
– Manu Mar 16 '17 at 18:59

Using StreamPlot and Manipulate to show the field lines with varying the parameters

1 Answers1

Linked