Let $x_1(x), x_2(x), x_3(x)$ satisfy the system $$\begin{cases} x_1' = -2x_1+x_2x_3 \\ x_2' = x_1 - x_1x_3 \\ x_3' = x_1x_2 \end{cases} $$ Construct a Lyapunov function to show that the origin is stable. Is the origin asymptotically stable?
I tried $V = x_1^2 + 2x_2^2 + x^2_3$ and get $V' = -4x_1^2 + 4x_1x_2$, which isn't successful. A lot of my other tries would cause $V$ failed to be positive definite.