Question: Construct a Lyapunov function for the system [ begin{aligned} & dot{x}_{1}=x_{1}^{2}+x_{2}^{2}-x_{1} & dot{x}_{2}=x_{1}^{2}-x_{2}^{2}-x_{2} end{aligned} ] and use it to investigate the stability at the

Construct a Lyapunov function for the system

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

and use it to investigate the stability at the origin. State the domain of attraction if the system is asymptotically stable.

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