Poincaré-Bendixson Theorem - Dynamical Systems | Lecture 24

For the past few lectures we have been focusing on limit cycles in planar dynamical systems. In particular, we have looked at how to rule them out. In this lecture we take a more positive turn and show how the Poincaré-Bendixson theorem can be applied to prove their existence. We walk through two examples together to prove the existence of a stable limit cycle solution. The second of which is a model for glycoloysis due to Sel'kov (1968).

Some further references for the Poincaré-Bendixson theorem presented at varying degrees of complexity:

This course is taught by Jason Bramburger for Concordia University.

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[hanshearth]

Thanks for the great lecture. I do have to point out that at min 37:40, you had it backwards. When the trace is positive, the fixed point is unstable and vice versa.
This error carries over to your plot, trace<0 stable LC, and trace>0 stable fp

Thank you profesor Jason Bramburger. Greetings from Bimac Research Group at Universidad del Cauca, Colombia.

[muzafferoz]

what is the book that you suggest for the Poincare- Bendixson theorem as a second source ?