A nonlinear system is described by the following equations,

\[
\begin{aligned}
& \dot{x}_{1}=2 x_{1}+3 x_{1}^{2}-2 x_{2}+u \\
& \dot{x}_{2}=x_{2}-0.25\left(\sin x_{1}+\cos x_{2}ight)+u .
\end{aligned}
\]

(a) With \(u=0\) plot the state-space trajectories in the neighbourhood of the origin defined by \(\left|x_{1}ight| \leq 1,\left|x_{2}ight| \leq 2\).

(b) Using Lyapunov's first method, linearise the above system about \(x_{1}=x_{2}=u=0\), and assess the stability of this linearised system.