I'm reading about the Poincaré-Bendixson theorem in the plane, I really liked the theorem. I have seen common applications in Sotomayor and Perko's book. But I would like to know what other applications outside of the common literature (mentioned above) there are, I mean interesting applications that you create valuable. If possible, mention a reference to your example. Thank you very much.

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    $\begingroup$ this is really way too unfocused for this site. $\endgroup$ Mar 10 at 15:34
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    $\begingroup$ A related question on math.stackexchange: math.stackexchange.com/questions/326351/… $\endgroup$
    – AGenevois
    Mar 10 at 16:19
  • $\begingroup$ Does periodicity for solutions of the Lotka-Volterra equations count? Though there are more elementary arguments for that. $\endgroup$
    – ThiKu
    Mar 11 at 15:36
  • $\begingroup$ Now I am busy with work, later I will edit my question to list all the applications that I have managed to find along with your reference, I think that way you could help me much better. $\endgroup$
    – Zaragosa
    Mar 11 at 21:03