Limit Cycles, Part 2: Analytical Tests for Limit Cycles- Lyapunov Functions, Dulac's Criterion

[@michaelzumpano7318]

I really like the fact that you are saying exactly what is in your head without any translation. It makes it very easy to follow your thought processes. Your videos are a nice balance between rigor and first-time learning. They’re hard to stop watching.

[@ProfessorRoss]

Thank you Michael. I'm glad my teaching style fits your learning style. Enjoy!

[@jimmyphilip8847]

Your videos are extremely helpful!

[@ProfessorRoss]

Thanks!

[@ivanluthfi8832]

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[@mohamedradwan7634]

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[@ProfessorRoss]

You're welcome!

[@brendawilliams8062]

Lots better than the language of well

[@nagesheranki3933]

Hi! Can we have Liapunov functions whose level sets are not necessarily a single closed curve? I feel like the whole idea behind Liapunov functions is to verify that the vector field along all closed curves points "inward" towards the fixed point(much like the figure in Wiggins). So I'm wondering if this method fails if the Liapunov function has level sets that are two separate closed curves.

[@ProfessorRoss]

I think a candidate Lyapunov function has to be positive definite which would rule out having level sets that are separate. If you have such a function, you could limit the domain of the Lyapunov function to just the interior of one of the level sets.

[@brendawilliams8062]

Thankyou