Lyapunov-Function with the Method of Aizermann/Krasovski

Question

Consider the following autonomous system:

$$ \begin{align} \dot{x}_1 &= -2 x_1 \\ \dot{x}_2 &= -2 x_2 + 2 x_1 x_2^2 \end{align} $$

Derive for the equlibrium $x_1 = x_2 = 0$ a Lyapunov-function and its domain with

1. the Method of Aizermann (linearization), and
2. the Method of Krasovski.