0
$\begingroup$

Recently, I was trying to understand the concept of Phase diagram. I found that they are only useful in visualizing the solutions of scalar autonomous ODEs and not suitable for investigating non-autonomous ODEs. My questions are,

  1. Why we can use the phase diagram technique only for autonomous equations and not for non-autonomous equations?
  2. Is there any other method available to visualize the solutions of non-autonomous ODEs?

Please let me know for any other information. Thanks in Advance.

$\endgroup$
0
$\begingroup$

Let $x_1(t)$ and $x_2(t)$ be two solutions of an autonomous system. If $x_1(t_1)=x_2(t_2)$, then $x_2(t)=x_1(t+t_1-t_2)$. This implies that trajectories do not cross. This is no longer true for non autonomous systems, making it impossible to draw a meaningful phase diagram.

$\endgroup$

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.