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

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}]

• How does your function depend upon $y$? – David G. Stork Mar 16 '17 at 18:43
• It only depends on x, no y. – Manu Mar 16 '17 at 18:46
• 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

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[

• 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