0
$\begingroup$

Determine all resting positions for differential equation $x'=f(x,\mu)$. Examine whether the resting positions are attractive or repulsive.

$x'=x^2-\mu$

Make a sketch in the plane $(\mu,x)$ where the corresponding resting positions are drawn on vertical lines $\mu=const$ and the behavior of the solutions for the respective value are shown with arrays.

Note: Branching diagram.

Solution:

$x=+-\sqrt(\mu)$

$f(x)=x^2-\mu$

$f'(x)=2x$

$f(-\mu)=-2\sqrt\mu$ attractive

$f(\mu)=2\sqrt\mu$ repulsive.

But how do I make sketch?

$\endgroup$
1
$\begingroup$

This is an option

enter image description here

The dashed line shows that branch is unstable, and the solid line that it is stable

This script will help you generate your own version the plot

$\endgroup$

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.