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.
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$\begingroup$ What does $(x/6)6$ mean? Isn't that just $\frac{6x}{6} = x$? $\endgroup$– Matthew CassellMar 6, 2015 at 13:20
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$\begingroup$ Sorry, I rewrite the question. $\endgroup$– metamodeMar 7, 2015 at 6:25
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