For the following system, determine the equilibrium points and discuss the stability of each equilibrium using Lyapunov's (indirect) linearisation method.

\[
\begin{aligned}
& \dot{x}_{1}=x_{1}-x_{1}^{2}-\frac{1}{2} x_{1} x_{2} \\
& \dot{x}_{2}=x_{2}-x_{2}^{2}+\frac{1}{2} x_{1} x_{2} .
\end{aligned}
\]

Sketch the flow of trajectories in the \(\left(x_{1}, x_{2}ight.\) ) phase plane and classify each equilibrium point (for example, node or saddle).