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About LinkBacksFor dx/dt = y^3 - 2*x^3
dy/dt = -3*x - y^3
Show that the origin is nonlinearly stable by nding the appropriate Lyapunov function.
Hey, I don't have it but let me try to rough it in ok:
So we have:
In these, sometimes we can find a Lyapunov function of the formfor suitable choices of a and b such that
at the critical point
,
if
in some region about
in that same region. If so, then the point
and
and then:
The last term is always negative. However, I can't show that for suitable choices of a and b, the entire expression is less than or equal zero in some deleted neighborhood of the origin.
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