Lyapunov Functions

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We discuss how Lyapunov functions can be used to prove the asymptotic stability of a critical points of nonlinear systems of differential equations.

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  1. Mike, the Mathematician
  2. mike the mathematician
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Excellent video. Thank you very much!

kktech
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Excellent video, any reason we take L=x^2+y^2? Is it a rule of thumb or is there some thought behind it?

andrewabourachid
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Firstly, really useful video, gives great intuition behind this.
At 6:33 you say that the lyapunov function has to be always positive. If our L(x, y) was x^2+y^2 - 1, (the same 3d graph as the one in the video but shifted one unit down the z axis), the reasoning is still the same, so, couldn't we conclude the same thing (i.e origin is asymptotically stable)? Why is it a necessary requirement for L(x, y) >= 0?

wast
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This is really informative. Your board squeaks A LOT though.

jeremydening