For a system
$$x'=-x^4+2x^5+y$$
$$y'=-x^5-y.$$
I found the Liapunov function as $$V(x,y)=(x+y)^2+2((x^5)/5-(x^6)/6)$$.
A domain of asymptotic stability will be the interior of the largest level curve
which is within $$-1<x<1$$
Now, I cannot proceed since I couldn't find the simple closed curve by using this Liapunov function. Any helps will be appreciated.
2026-04-01 17:27:55.1775064475
A Domain of Asymptotic Stability
87 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
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