Let $V$ is a Lyapounov function $V(x,y) = 3x^2 - 2xy + y^2$, $\dot{V}(x,y) = -2(x+1)(x^2+y^2)$. I need to find its domain of attraction.
The minimum of $V$ is $x = -1$, so $\theta (y)$ $ = 3 + 2y + y^2$, min $\theta$ = 2 and $y = -1$
From here, the domain of attraction is $D = {(x,y): 3x^2 - 2xy + y^2 < 2}$
Also I tried to draw the domain of attraction. Could someone look if I'm doing it right?
Hint.
Putting in the same plot $V(x,y) > 0$ (black) and $\dot V(x,y) < 0$ (blue) we obtain